JP7108185B2 - Optimizer and method of controlling the optimizer - Google Patents

Description

The present invention relates to an optimization device and a control method for the optimization device.

In today's society, information processing is performed in every field. These information processes are performed by computing devices such as computers, and prediction, determination, control, etc. are performed by computing and processing various data and obtaining meaningful results. One of these information processes is optimization, which is an important field. For example, the problem of finding a solution that minimizes the resources and costs required to do something, or maximizes its effectiveness, and it is clear that these are very important.

Among optimization problems, many of the problems called discrete optimization problems and combinatorial optimization problems are known to be extremely difficult to solve because variables take discrete values rather than continuous values. . The biggest reason why it is difficult to solve a discrete optimization problem is that there are a large number of states called local solutions that are not optimal solutions but take the minimum value in the local neighborhood.

Since there is no efficient general method for solving discrete optimization problems, it is necessary to use an approximate solution method that utilizes the unique properties of the problem or a method called meta-heuristic that does not rely on the properties of the problem.

The following description relates to the solution using the Markov chain Monte Carlo method among the latter, and particularly to the quasi-annealing method in a broad sense called the exchange Monte Carlo method or the replica exchange method.

The pseudo-annealing method is a method of obtaining an optimum solution by stochastically changing the state (value of variable vector) using random numbers. In the following, the problem of minimizing the value of an evaluation function to be optimized will be described as an example, and the value of the evaluation function will be called energy. For maximization, the sign of the evaluation function should be changed.

In the pseudo-annealing method, if the probability of accepting (allowing) a state transition is determined using the energy change and temperature associated with the transition as follows, the state reaches the optimal solution at the limit of infinite time (number of iterations) proven to do.

Equation (2) is the Metropolis method. Equation (3) is the Gibbs method. Either one of the expressions (2) and (3) is used.
Here, T is a parameter representing temperature, and its initial value must be set sufficiently large according to the problem, and it must be lowered sufficiently slowly.

As described above, in the pseudo-annealing method, the optimal solution can be obtained by taking an infinite number of iterations, but in reality, it is necessary to obtain the solution with a finite number of iterations, so the optimal solution cannot be reliably obtained. Moreover, since the temperature drops very slowly as described above, the temperature does not drop sufficiently in a finite amount of time. Therefore, practical quasi-annealing methods often decrease the temperature faster than the temperature change that is theoretically guaranteed to converge.

In the actual pseudo-annealing method, starting from the initial state, the above iterations are repeated while decreasing the temperature. finish. The output answer is the state at the end. However, in reality, the temperature does not become 0 in a finite number of iterations, so even at the end the probability of occupancy of the state has a distribution represented by the Boltzmann distribution, etc., and it is not necessarily the optimum value or a good solution. do not have. Therefore, a realistic solution is to hold the state with the lowest energy obtained so far during the iteration and output it at the end.

As can be imagined to some extent from the above explanation, the pseudo-annealing method is versatile and very attractive, but there is a problem that the calculation time is relatively long due to the need to lower the temperature slowly. Furthermore, there is also the problem that it is difficult to appropriately adjust how to lower the temperature according to the problem. If the temperature is lowered too slowly, the temperature will not drop so much in a finite time, so the energy range of the final heat distribution will be widened and the probability of good solutions will not increase. Conversely, if the temperature is lowered too quickly, the temperature will drop before escaping from the local minimum, and the bad solution will remain trapped, reducing the probability of obtaining a good solution.

In the replica exchange method, a Monte Carlo search using multiple temperatures (hereinafter referred to as "probabilistic search") is performed at the same time. is a method of performing an operation of exchanging

FIG. 25 is a diagram showing a configuration example of an optimization device using a normal replica exchange method. The optimization device 50 has a plurality of replicas (searching units 51a1, 51a2, . . . , 51ai, . . The exchange control unit 52 provides the searching units 51a1 to 51an with temperature information (hereinafter referred to as inverse temperature βi (reciprocal of T) (1≤i≤n)).

FIG. 25 shows an example of the searching unit 51ai. Other search units have the same configuration. The search unit 51ai has a state holding unit 60 , an energy calculation unit 61 and a transition control unit 62 .
The state holding unit 60 holds the values of multiple state variables included in the evaluation function. Further, the state holding unit 60 stores values of a plurality of state variables (values of the variable vector) based on a flag f indicating whether or not state transition is possible and a number (index) N of the state variable indicated by the flag f. Update state s _i .

The energy calculator 61 calculates energy changes associated with changes in state variables (state transitions). For example, when the evaluation function is represented by an Ising model represented by a connection between two state variables and only one state variable transition is allowed at a time, the energy calculation unit 61 calculates the value of each state variable and the state An energy change associated with each change (state transition) of a plurality of state variables is calculated based on the coupling coefficient indicating the strength of coupling between variables, the number N, and the flag f. The energy change ΔE _ij indicates the energy change accompanying the change of the j-th state variable. Note that the values of the coupling coefficients corresponding to the optimization problem to be calculated are stored in advance in a memory, a register, or the like. When the evaluation function is not the Ising model and when multiple state variables are allowed to transition at once, the state transition number and the changing state variable number do not necessarily match, but the energy change with respect to the state transition number is appropriately calculated. It would be nice if it could be calculated. The energy calculator 61 can be implemented using a logic circuit such as a sum-of-products arithmetic circuit, for example.

The transition control unit 62 uses the energy change ΔE _ij and the inverse temperature β _i assigned by the exchange control unit 52 to calculate the acceptability probability of the state transition of the j-th state variable as follows, similarly to the normal pseudo-annealing method. A probabilistic search is performed by determining by Equation (4).

In equation (4), the function f is the same as in equation (1), and for example, the metropolis method of equation (2) is used. The transition control unit 62 outputs a flag f indicating whether the state transition is possible or not, and the number of the state transition indicated by the flag f, based on the acceptance probability of the state transition. Also, the transition control unit 62 updates and outputs the energy E _i based on the energy change ΔE _ij .

The exchange control unit 52 observes the energy E in each search unit for each fixed number of iterations, and uses the energy E and the inverse temperature β in two of the search units 51a1 to 51an, and expresses the following equation (5): Swap the value of each state variable in the two search units based on the exchange probabilities obtained. Instead of the value of the state variable, the inverse temperatures supplied to each of the two search units may be exchanged.

In equation (5), β _i is the inverse temperature given to the search unit 51ai, β _j is the inverse temperature given to the j-th search unit (not shown), E _i is the energy in the search unit 51ai, and E _j is It is the energy in the j-th search unit. Also, in equation (5), the function f is the same as in equation (1), and for example, the Metropolis method of equation (2) is used.

Even if such an exchange is performed, the probability distribution of the state of each temperature converges to the Boltzmann distribution for that temperature. And the relaxation time required to converge to this distribution can be significantly shorter than without exchange.

Note that two search units to be exchanged are selected so that the temperature supplied is close (for example, the one supplied with adjacent temperatures) so that the exchange probability does not become too small.
In the optimization device 50, when the search units 51a1 to 51an that perform a large number of iterative processes are realized by dedicated circuits, and the functions of the exchange control unit 52 are realized by software, two search units with similar temperatures can be obtained by passing pointers. , the value of each state variable (or temperature information) may be exchanged. In this case, sorting processing for arranging the information identifying the search units 51a1 to 51an in ascending or descending order of temperature for each replacement need not be performed.

For example, an information processing apparatus has been proposed that performs probabilistic searches in a plurality of networks (called an ensemble) in which different temperatures are set (see, for example, Patent Document 1). The proposed information processing apparatus exchanges the states of the nodes of each ensemble according to the difference in the energy of each ensemble between the ensembles whose temperatures are set adjacent to each other. As a result, falling into a local optimum is prevented, and convergence to the optimum value is made faster.

Further, a constant temperature for temperature parallel simulated annealing for changing a parameter for controlling execution of the simulated annealing algorithm so that the simulated annealing processing means operates efficiently under the first temperature A tank apparatus has been proposed (see Patent Document 2, for example). The proposed apparatus performs a simulated annealing process under set conditions, and the state obtained as a result of this simulated annealing process is subjected to a simulated annealing process at a second temperature. Probabilistically exchanges with the state obtained by

For each gene belonging to any generation after the initial generation or the second generation, a frequency distribution on a plane spanned by two axes of Hamming distance and fitness is obtained, and parameters of the genetic algorithm are determined according to this frequency distribution. There is also a proposal for an analysis system that changes the (see, for example, Patent Document 3).

JP 2018-5541 A JP-A-9-231197 JP-A-9-325949

When a stochastic search is performed by a plurality of search units set to different temperatures as described above, there is a problem that the solution-finding performance is degraded depending on the temperature set for each search unit.
In one aspect, an object of the present invention is to provide an optimization device and a control method for the optimization device that can improve solution accuracy.

In one aspect, an optimization device is provided that has a plurality of search units and a control unit that controls the plurality of search units. Each of the plurality of search units includes a state holding unit that holds values of a plurality of state variables included in the evaluation function representing the energy value, and a state transition according to a change in any of the values of the plurality of state variables. occurs, based on the energy calculation unit that searches for the ground state by calculating the change value of the energy value for each of a plurality of state transitions, and the set temperature value, the change value, and the random value, the energy a transition control unit that stochastically determines whether to accept any one of the plurality of state transitions based on the relative relationship between the value change value and the thermal excitation energy. The control unit acquires temperature statistical information, which is statistical information about temperature value transitions in each of the plurality of search units, and determines a temperature value to be set in each of the plurality of search units based on the acquired temperature statistical information. a temperature controller that sets the determined temperature value to each of the plurality of search units; or an exchange control unit that exchanges the values of the plurality of state variables.

Also, in one aspect, a control method for an optimization device is provided.

On one side, solution accuracy can be improved.

It is a figure which shows the optimization apparatus of 1st Embodiment. It is a figure which shows the example of a circuit configuration of an optimization apparatus. 3 is a diagram showing a circuit configuration example of a state transition determination circuit; FIG. 3 is a diagram showing a circuit configuration example of a selector unit; FIG. It is a figure which shows the circuit structural example of a temperature control part. FIG. 4 is a diagram showing an example of data stored in a register; FIG. FIG. 4 is a diagram showing an example of a data acquisition algorithm; FIG. 5 is a diagram showing an example of changes in minimum energy and temperature; FIG. 4 is a diagram showing an example of a temperature histogram; FIG. 4 is a diagram showing an example of a cumulative histogram; FIG. 11 is a flowchart showing an example of overall control of replica exchange; FIG. 9 is a flow chart showing an example of search unit processing; It is a flow chart which shows an example of data collection processing. 6 is a flow chart showing an example of exchange control; It is a figure which shows the example (1) of the flow of a process. FIG. 10 is a diagram showing an example (part 2) of the flow of processing; It is a figure which shows the other hardware example of an optimization apparatus. It is a figure which shows the circuit structural example of the optimization apparatus of 2nd Embodiment. It is a figure which shows the circuit structural example of a temperature control part. FIG. 4 is a diagram showing an example of data stored in a register; FIG. FIG. 11 is a flowchart showing an example of overall control of replica exchange; FIG. It is a flow chart which shows an example of data collection processing. 6 is a flow chart showing an example of exchange control; FIG. 10 is a diagram showing an example of the number of solutions; FIG. 10 is a diagram showing a configuration example of an optimization device using a normal replica exchange method;

Hereinafter, this embodiment will be described with reference to the drawings.
[First embodiment]
A first embodiment will be described.

FIG. 1 is a diagram showing an optimization device according to the first embodiment.
The optimization device 1 has a plurality of search units (search units 10a1, 10a2, . . . , 10aN) and a control unit 20. FIG. N is an integer of 2 or more and corresponds to the number of search units. Each of search units 10a1 to 10aN has a state holding unit, an energy calculation unit, and a transition control unit. For example, search unit 10 a 1 has state holding unit 11 , energy calculation unit 12 and transition control unit 13 .

The state holding unit 11 holds the values of a plurality of state variables included in the evaluation function representing the energy value. In FIG. ₁ , the energy value in the search unit 10a1 is represented by E1, and the values of the plurality of state variables in the search unit _10a1 are represented by s1.

The energy calculation unit 12 calculates an energy value change value (ΔE _1j ) for each of the plurality of state transitions when the state transition occurs in response to a change in any of the plurality of state variable values. A ground state search is performed by

Based on the set temperature value, the change value, and the random value, the transition control unit 13 determines whether or not to accept any one of the plurality of state transitions according to the relative relationship between the change value of the energy value and the thermal excitation energy. to decide As described above, the transition control unit 13 determines whether or not the state transition is possible based on the equation (4), and outputs the flag f indicating whether or not the state transition is possible and the number of the state transition indicated by the flag f. In FIG. 1, the index indicates the state transition number indicated by the flag f.

The search units 10a1 to 10aN operate in parallel to perform the above ground state search.
The control unit 20 controls the search units 10a1 to 10aN. The control section 20 has a temperature adjustment section 21 , a temperature control section 22 and an exchange control section 23 .

The temperature adjustment unit 21 acquires temperature statistical information, which is statistical information about the transition of temperature values in each of the search units 10a1 to 10aN, and adjusts the temperature to be set for each of the search units 10a1 to 10aN based on the acquired temperature statistical information. determine the value. Since the number of searching units 10a1 to 10aN is N, the number of temperature values to be set is N. The N temperature values are different from each other. For example, the temperature _values may _be the _{inverse temperatures β 1} , _{β 2} , .

The temperature control unit 22 sets the determined temperature value to each of the search units 10a1 to 10aN.
The exchange control unit 23 exchanges the temperature values or the values of the plurality of state variables between the plurality of search units after reaching the number of repetitions of the search for the ground state of the energy value or after a certain period of time has elapsed. Exchange control unit 23 _acquires energy values E ₁ , E ₂ , . Decide whether to replace or not. Alternatively, instead of determining whether or not to exchange the temperature values between the search units, the exchange control unit 23 determines whether or not to exchange the values of the plurality of state variables between the search units based on Equation (5). You may

Here, an example of temperature determination by the temperature adjustment unit 21 will be described. For example, the temperature adjustment unit 21 searches the acquired temperature statistical information for the temperature value corresponding to the maximum appearance frequency in the temperature frequency information obtained by counting the appearance frequency of each temperature value regarding the transition of temperature values. to 10aN, respectively.

More specifically, when the minimum value of the energy value is updated in any of the search units, the temperature adjustment unit 21 changes the minimum value of the energy value from the previous update to the current update. Gets the highest temperature value among the temperatures set in , as temperature statistical information. For example, the temperature adjustment unit 21 identifies the temperature value with the highest frequency of appearance in a histogram obtained by counting the frequency of appearance of the acquired temperature values, and based on the identified temperature value, the search units 10a1 to 10aN Calculate the temperature values to be set for each of the

In one example, the temperature adjuster 21 calculates the i-th temperature tmp[i] (i=1, 2, . . . , N) of the N temperature values using equations (6) and (7).

max_tmp is the maximum value of the set temperature, and is the temperature value that appears most frequently in the histogram. min_tmp is the minimum value of the set temperature and is given in advance. In this way, the temperature adjustment unit 21 determines the maximum temperature value max_tmp from the acquired temperature statistical information, and determines the temperature values to be set in each of the search units 10a1 to 10aN based on the maximum value max_tmp. The reason why the maximum setting temperature max_tmp is set to the temperature value with the highest appearance frequency in the temperature statistical information as described above is that the energy value of the search unit can be reduced by using the temperature value with the highest appearance frequency as the highest value. This is because it is estimated that there is a high possibility that the minimum value of can be updated. However, the maximum value max_tmp may be, for example, a temperature that is higher by a predetermined value (or a predetermined ratio) than the temperature value with the highest appearance frequency.

Alternatively, the temperature adjustment unit 21 adds a predetermined coefficient to the maximum value of the cumulative frequency in the temperature cumulative frequency information representing the cumulative frequency of occurrence of each temperature value regarding the transition of the temperature value among the acquired temperature statistical information. A temperature value corresponding to the frequency obtained by multiplication may be set in each of the search units 10a1 to 10aN.

More specifically, the temperature adjustment unit 21 acquires, as the temperature cumulative frequency information, the cumulative frequency of appearance of each temperature value in the histogram, starting from the lowest temperature value. Then, the temperature adjustment unit 21 specifies a temperature value corresponding to the frequency obtained by multiplying the maximum value of the cumulative frequency in the cumulative histogram representing the cumulative frequency by a predetermined coefficient, and based on the specified temperature value, the search units 10a1 to 10aN Calculate the temperature values to be set for each of the That is, the temperature adjustment unit 21 uses the specified temperature value as the maximum value max_tmp, and calculates the temperature tmp[i] by the formulas (6) and (7).

Note that the temperature tmp[i] (temperature value) determined by the temperature adjustment unit 21 may be set by the temperature control unit 22 to each of the search units 10a1 to 10aN.
Further, the temperature adjustment unit 21 acquires the energy value from each of the search units 10a1 to 10aN after the number of repetitions of the search for the ground state of the energy value has been reached or after a certain period of time has elapsed, and determines whether or not the minimum value of the energy value has been updated. , for each of the plurality of search units. For example, the temperature adjustment unit 21 causes the exchange control unit 23 to exchange the temperature values (or the values of the plurality of state variables) between the plurality of search units after reaching the number of repetitions of the search for the ground state of the energy value or after a certain period of time has elapsed. , it is checked whether the minimum energy value has been updated.

Then, the temperature adjusting unit 21 acquires the temperature statistical information in a predetermined period during which the first temperature value is set in each of the searching units 10a1 to 10aN, and after the predetermined period ends, based on the temperature statistical information, the searching unit A second temperature value to be set for each of 10a1 to 10aN is determined.

For example, the temperature adjustment unit 21 acquires temperature statistical information in an initial partial period of the entire period of the ground state search by the search units 10a1 to 10aN, and determines the temperature tmp[i] based on the temperature statistical information. do. The control unit 20 uses the determined temperature tmp[i] to continue the ground state search by the search units 10a1 to 10aN in the remaining period.

Alternatively, the temperature adjustment unit 21 may acquire the temperature statistical information for each predetermined partial period for the entire period of the ground state search by the search units 10a1 to 10aN, and determine the temperature tmp[i] after the partial period. Then, the control unit 20 uses the temperature tmp[i] determined based on the temperature statistical information acquired in the previous partial period in the next partial period to continue the ground state search by the search units 10a1 to 10aN. good too.

Here, the "period" may be determined by the number of repetitions of the ground state search by the search units 10a1 to 10aN, or may be determined by a time interval.
By the way, it is conceivable to perform the optimization operation using the replica exchange method as described above. In the replica exchange method, ground state searches are performed at different temperatures in a system called a plurality of replicas. It is a method of exchanging variable values). According to the replica exchange method, even if a local solution is reached when the temperature drops, the replica exchange can raise the temperature to a higher temperature and search for the global solution again. Desired. However, it is necessary to appropriately determine the temperature to be set for each replica, and if the temperature (especially the maximum temperature) is too high or too low, the accuracy of the solution will drop and the search will take a long time. In addition, in order to appropriately determine the temperature, if optimization calculations are performed many times using a number of temperature parameters, it takes a great deal of time and effort, impairing the user's convenience.

In the optimization device 1, as described above, the statistical information of the maximum temperature reached by the replica (for example, the search unit) is acquired while the minimum energy of the replica is updated, and based on the statistical information, the search units 10a1 to Determine a set temperature of 10 aN. In this manner, the optimization device 1 can improve solution accuracy by adaptively determining temperatures to be used in subsequent calculations based on temperature statistical information acquired in the actual calculation process. Also, the speed of calculation can be increased. That is, the solution-finding performance is improved. Furthermore, it is possible to save the trouble of adjusting the temperature, thereby improving the user's convenience.

Next, a circuit configuration example of the optimization device 1 will be described. A case where the optimization problem is represented by an Ising model will be exemplified below. First, a case of exchanging temperatures in the search units 10a1 to 10aN will be exemplified. After that, as a second embodiment, a case of exchanging the values of a plurality of state variables in the search units 10a1 to 10aN will be exemplified.

FIG. 2 is a diagram showing a circuit configuration example of the optimization device.
When the optimization device 1 has the minimum value among the combinations (states) of the values of a plurality of spin bits corresponding to a plurality of spins included in the Ising model into which the optimization problem to be calculated is transformed, Search for the value (ground state) of each spin bit of .

The Ising-type evaluation function E(x) is defined, for example, by the following equation (8).

The first term on the right side is the product of the value of two spin bits (0 or 1) and the coupling coefficient without omission or duplication for all combinations of two spin bits that can be selected from all spin bits included in the Ising model. It is an accumulated value. Assume that the total number of spin bits included in the Ising model is n (n is an integer of 2 or more). For example, n=1024. Also, each of i and j is an integer of 1 or more and n or less. x _i is a variable (also called a state variable) representing the value of the i-th spin bit. x _j is a variable representing the value of the jth spin bit. W _ij is a weighting factor that indicates the magnitude of interaction between the i-th and j-th bits. Note that W _ii =0. Also, W _ij =W _ji often holds (that is, the coefficient matrix of the weighting factors is often a symmetric matrix).

The second term on the right side is the sum of the products of the bias coefficients of all spin bits and the value of the spin bits. b _i indicates the bias coefficient of the i-th spin bit.
Also, when the value of the variable x _i changes to 1−x _i , the increment of the variable x _i can be expressed as δx _i =(1−x _i )−x _i =1−2x _i . Therefore, the energy change ΔE _i associated with the spin reversal (value change) is expressed by the following equation (9).

h _i is called a local field (local field) and is represented by Equation (10).

The energy change ΔE _i is obtained by multiplying the local field h _i by a sign (+1 or −1) according to δx _i . A change δh _i ^(j) of the local field h _i when a certain variable x _j changes is expressed by Equation (11).

The process of updating the local field h _i when a certain variable x _j changes is performed in parallel for each variable.
The optimization device 1 is implemented using a semiconductor integrated circuit such as an FPGA (Field Programmable Gate Array), for example. The optimization device 1 has an overall control unit 24 in addition to the search units 10a1 to 10aN, the temperature adjustment unit 21, the temperature control unit 22, and the replacement control unit 23 illustrated in FIG. In addition, in the example of FIG. 2, since the replacement control unit 23 is included in the temperature control unit 22, illustration of the replacement control unit 23 is omitted.

Each of the search units 10a1 to 10aN implements a ground state search based on the Ising type evaluation function represented by Equation (8) using the following circuit. Although the search section 10a1 will be mainly described below, the search sections 10a2 to 10aN have the same circuit configuration.

, 12bn, ΔE generators 12c1, 12c2, . . . , 12cn, adders 13a1, 13a2, . , state transition determination circuits 13b1, 13b2, .

In FIG. 2, the names of the h calculators 12b1 to 12bn are given with subscripts such as "h _i " calculator so that it is easy to understand that they correspond to the i-th spin bit. Also, in FIG. 2, the ΔE generation units 12c1 to 12cn are named with subscripts such as “ΔE _i ” calculation unit so that it is easy to understand that they correspond to the i-th spin bit. .

The process of determining whether to invert any spin bit contained in a spin bit string in a search unit and inverting the corresponding spin bit when inverting is a ground state search (also referred to as a stochastic search) by the search unit. There is one time of processing.

Registers 12a1-12an, h calculators 12b1-12bn, and ΔE generators 12c1-12cn correspond to the energy calculator 12. FIG. That is, the energy calculator 12 has registers 12a1-12an, h calculators 12b1-12bn, and ΔE generators 12c1-12cn. The adders 13a1-13an, the state transition determination circuits 13b1-13bn, the selector section 13c and the offset control section 13d correspond to the transition control section 13. FIG. That is, the transition control section 13 has adders 13a1 to 13an, state transition determination circuits 13b1 to 13bn, a selector section 13c and an offset control section 13d.

Of the n spin bits, the register 12a1, the h calculator 12b1, the ΔE generator 12c1, the adder 13a1, and the state transition determination circuit 13b1 perform operations on the first spin bit. Also, the register 12a2, the h calculator 12b2, the ΔE generator 12c2, the adder 13a2, and the state transition determination circuit 13b2 perform calculations regarding the second spin bit. Similarly, a numerical value i at the end of a code such as "12a1" or "12b1" indicates that an operation corresponding to the i-th spin bit is performed. That is, one search unit is a set of a register, an h calculation unit, a ΔE generation unit, an adder, and a state transition determination circuit (one unit of an arithmetic processing circuit that performs operations related to one spin bit, and is called a “neuron”). There is also n). The n sets operate in parallel on the spin bits corresponding to each set.

In the following, the register 12a1, the h calculator 12b1, the ΔE generator 12c1, the adder 13a1, and the state transition determination circuit 13b1 will be mainly described as examples. Registers 12a2 to 12an, h calculators 12b2 to 12bn, ΔE generators 12c2 to 12cn, adders 13a2 to 13an, and state transition determination circuits 13b2 to 13bn, which have the same name, have the same function.

Here, the spin bit corresponding to the set of the register 12a1, the h calculation unit 12b1, the ΔE generation unit 12c1, the adder 13a1, and the state transition determination circuit 13b1 is the own spin bit, and the other spin bits calculated by the search unit 10a1 are It is called another spin bit. Each spin bit is identified by identification information called an index. For example, the index of the i-th spin bit is i.

Register 12a1 stores a weighting factor W _1j (j=1 to n) between its own spin bit and other spin bits. Here, the total number of weighting factors is n2 for the number of spin bits ⁿ . Register 12a1 stores n weighting factors. The subscript i of the weighting factor W _ij indicates the index of the own spin bit, and the subscript j indicates the index of any spin bit including the own spin bit.

The register 12a1 stores n weighting factors W ₁₁ , W ₁₂ , . . . , W _1n for the own spin bit. Note that W _ii =W ₁₁ =0. The register 12a1 outputs the weighting factor _W1j corresponding to index=j output from the selector 13c to the h calculator 12b1.

The h calculator 12b1 uses the weighting factor _W1j supplied from the register 12a1 to calculate the local field h1 based on equations ( ₁₀ ) and (11). For example, the h calculator 12b1 has _a register that holds the previously calculated local field h1, and multiplies _h1 by _δh1 ^(j) corresponding to the spin bit inversion direction indicated by index=j. Thus, _h1 stored in the register is updated. A signal indicating the reversal direction of the spin bit indicated by index=j may be supplied from the state holding unit 11 to the h calculating unit 12b1. _The initial value of h1 is preset in the register of the h calculator 12b1 depending on the problem. Also, the value of b1 is preset in the register of the h calculator 12b1 depending _on the problem. The h calculator 12 b 1 outputs the calculated local field h ₁ to the ΔE generator 12 c 1 and the E calculator 14 .

The ΔE generating unit _12c1 uses the local field h1 to generate an energy change value _ΔE1 of the Ising model according to the inversion of its own spin bit based on Equation (9). For example, the ΔE generation unit 12c1 may determine the inversion direction of the own spin bit from the current value of the own spin bit supplied from the state holding unit 11 (if the current value is 0, the inversion direction is from 0 to 1). , and if the current value is 1, the direction of reversal is from 1 to 0). The ΔE generator 12c1 outputs the generated energy change value _ΔE1 to the adder 13a1. Here, according to the addition processing in the adder 13a1 and the determination processing in the state transition determination circuit 13b1 in the subsequent stage, the ΔE generation unit 12c1 reverses the sign of the energy change value ΔE ₁ to generate the energy change value −ΔE ₁ as It may be output to the adder 13a1. In this example, the ΔE generator 12c1 outputs −ΔE ₁ to the adder 13a1 as the energy change value.

The adder 13a1 adds −ΔE ₁ supplied from the ΔE generator _12c1 and the offset value Eoff supplied from the offset controller 13d. The offset value E _off is a parameter for prompting state transition, as will be described later, and is controlled by the offset control unit 13d. In this example, E _off ≧0. The adder 13a1 outputs the addition result (-ΔE ₁ +E _off ) to the state transition determination circuit 13b1.

The state transition determination circuit _13b1 sets the flag f1 indicating whether or not the own spin bit can be inverted according to the sum of the energy change value supplied from the adder 13a1 and the offset ΔE _off (−ΔE ₁ +E _off ). output to Specifically, the state transition determination circuit 13b1 determines whether or not its own spin bit can be inverted according to the comparison between -ΔE ₁ +E _off and the threshold.

Here, determination by the state transition determination circuit 13b1 will be described.
In simulated annealing, the permissible probability p(ΔE, T) of state transition that causes a certain energy change ΔE is determined as in the above equation (1). In Equation (1), T is the temperature information T described above. The temperature information T is set in the state transition determination circuit 13b1 by the temperature control unit 22. FIG. Also, as the function f, equation (2) (Metropolis method) or equation (3) (Gibbs method) is used.

For example, a circuit that outputs a flag (flg=1) indicating that a state transition that causes an energy change ΔE with an allowable probability p (ΔE, T) is allowed is f (−ΔE/T) and an interval [0, 1 ) can be realized by a comparator that outputs a value corresponding to the comparison with the uniform random number u.

However, the same function can be realized even if the following modification is performed. Even if the same monotonically increasing function is applied to two numbers, the magnitude relationship does not change. Therefore, applying the same monotonically increasing function to the two inputs of the comparator does not change the output of the comparator. For example, the inverse function f ^-1 (-ΔE/T) of f(-ΔE/T) as a monotonically increasing function acting on f(-ΔE/T), and the monotonically increasing function f ^-1 f ⁻¹ (u), where −ΔE/T of (−ΔE/T) is u, can be used. In that case, the circuit having the same function as the above comparator may be a circuit that outputs 1 when -ΔE/T is greater than f ^-1 (u). Furthermore, since the temperature parameter T is positive, the state transition determination circuit 13b1 determines that when -ΔE is T·f ⁻¹ (u) or more (or ΔE is −(T·f ⁻¹ (u)) or less ), a circuit that outputs flg=1 may be used.

The state transition determination circuit 13b1 generates a uniform random number u and uses a conversion table for converting the value of f ⁻¹ (u) to generate the value of f ⁻¹ (u). If the Metropolis method is applied, f ⁻¹ (u) is given by equation (12). Also, when the Gibbs method is applied, f ⁻¹ (u) is given by equation (13).

The conversion table is stored, for example, in a register of the state transition determination circuit 13b1. The state transition determination circuit 13b1 generates the product (T·f ⁻¹ (u)) of the temperature parameter T and f ⁻¹ (u) as a threshold, and compares it with −ΔE ₁ +E _off . Here, T·f ⁻¹ (u) corresponds to thermal excitation energy. The state transition determination circuit 13b1 outputs a flag f ₁ =1 (transition allowed) to the selector section 13c when (−ΔE ₁ +E _off )≧T·f ⁻¹ (u). When (−ΔE ₁ +E _off )<T·f ⁻¹ (u), the state transition determination circuit 13b1 outputs a flag f ₁ =0 (transition impossible) to the selector section 13c.

The selector unit 13c receives flags indicating whether transition is possible or not output from each of the state transition determination circuits 13b1 to 13bn. If the flags output from each of the state transition determination circuits 13b1 to 13bn include flags indicating that the transition is permitted, the selector unit 13c selects any one flag that indicates that the transition is permitted. The selector unit 13c selects one predetermined flag when there is no flag indicating that transition is permitted among the flags output from each of the state transition determination circuits 13b1 to 13bn.

The selector unit 13 c outputs to the state holding unit 11 an update signal (update) including a flag indicating whether or not the transition is possible and index=j indicating the spin bit corresponding to the selected flag. At the same time, the selector unit 13c outputs the selected flag indicating whether or not the transition is permitted to the offset control unit 13d, and outputs index=j corresponding to the selected flag to each of the registers 12a1 to 12an.

The offset control unit 13d controls the offset value supplied to each of the adders 13a1 to 13an based on the flag indicating whether or not the transition is permitted, which is output from the selector unit 13c. Specifically, the offset control unit 13d resets the offset value to 0 when the flag output from the selector unit 13c indicates that the transition is permitted. The offset control unit 13d adds an increment value ΔE _off to the offset value when the flag output from the selector unit 13c indicates that transition is not possible. When the flag continuously indicates that transition is not possible, the offset control unit 13d increases E _off by ΔE _off by accumulating ΔE _off .

If the flag output from the selector unit 13c indicates that transition is not possible, it is considered that the current state falls into a local solution. By adding an offset value to -ΔE ₁ or increasing the offset value, the state transition becomes more permissible, and if the current state is in a local optimum, escape from the local optimum is facilitated.

The state holding unit 11 updates the bit _states (x ₁ , x ₂ , . Here, the bit state is a spin bit string (values of a plurality of state variables) including n spin bits in the search unit 10a1. In the figure, bit states are sometimes abbreviated as BS (Bit States). State holding unit 11 outputs the current bit state to E calculating unit 14 . The state holding unit 11 outputs to the general control unit 24 the bit state when the search processing in the search unit 10a1 is completed.

Based on the local fields h ₁ to h _n output from each of the h calculation units 12b1 to 12bn and the bit states (x ₁ to x _n ) output from the state holding unit 11, the E calculation unit 14 searches the search unit 10a1. _Compute the current energy value E1 of the Ising model at . _The energy value E1 is an energy value (sometimes simply referred to as energy) defined by the evaluation function of Equation (8). _The E calculator 14 outputs the calculated energy value E1 to the temperature controller 21 . Further, the E calculation unit ₁₄ outputs the calculated energy value E1 to the temperature control unit 22 when the searching unit 10a1 completes the searching process for a predetermined number of times or for a predetermined period.

Temperature adjustment unit 21 receives energy values E ₁ to E _N output from search units 10a1 to 10aN, respectively. Further, the temperature adjustment unit 21 acquires from the temperature control unit 22 information on the temperature set in each of the search units 10a1 to 10aN. FIG. 2 shows an example in which the temperature T ₁ is set for the search unit 10a1, the temperature T ₂ is set for the search unit 10a2, . . . , and the temperature _TN is set for the search unit 10aN. The temperature adjuster 21 generates new temperature information indicating a new temperature to be set to each of the search units 10a1 to 10aN according to changes in the energy values E ₁ to E _N and changes in the temperatures set to the search units 10a1 to 10aN. to decide. The temperature adjustment unit 21 outputs the determined new temperature information and a new temperature setting signal (T set sig. (sig. is an abbreviation for signal)) to the temperature control unit 22 .

The temperature control section 22 controls the temperature supplied to each of the searching sections 10a1 to 10aN. The temperature control unit 22 supplies temperature information indicating temperature and a temperature setting signal (T set sig.) to a state transition circuit included in each of the search units 10a1 to 10aN. Further, the temperature control unit 22 has the function of the exchange control unit 23, and controls temperature exchange (temperature exchange) in the search units 10a1 to 10aN (illustration of the exchange control unit 23 is omitted in FIG. 2). . The exchange control unit 23 determines whether or not to perform temperature exchange for a pair of search units (two search units) based on the exchange probability of Equation (5). The temperature control unit 22 supplies the temperature after replacement to each search unit.

For example, the exchange control unit 23 stores, in a register of the exchange control unit 23, first correspondence information that associates temperature identification information (referred to as temperature index or temperature number) with temperature. For example, temperature indices are associated with temperatures in ascending order of temperature (the higher the temperature index, the higher the temperature). Further, the exchange control unit 23 stores, in a register of the exchange control unit 23, second correspondence information in which the temperature indexes arranged in ascending order are associated with the identification numbers of the search units 10a1 to 10aN. In this case, a pair of search units corresponding to adjacent temperature indexes in the second correspondence information have adjacent set temperatures. The exchange control unit 23 controls temperature exchange for the search units 10a1 to 10aN based on the first correspondence information and the second correspondence information, and updates the second correspondence information according to the exchange. The temperature control unit 22 supplies the temperature to each search unit based on the first correspondence information and the second correspondence information. Note that the temperature associated with the temperature index in the first correspondence information is updated according to the calculation result of the new temperature by the temperature adjuster 21 .

However, the exchange control unit 23 holds correspondence information in which the identification numbers of the search units 10a1 to 10aN are associated with the temperature values, and sorts the correspondence information according to the temperature values so that the set temperatures are adjacent to each other. It is also possible to identify pairs of search units that In that case, the temperature value in the corresponding information is updated according to the calculation result of the new temperature by the temperature adjustment unit 21 .

The overall control unit 24 controls the overall operation of the optimization device 1 . Upon receiving the input of the activation signal, the overall control unit 24 outputs the activation signal to the temperature control unit 22, activates the search units 10a1 to 10aN, and starts the calculation of the ground state search for the optimization problem. After completing the calculation, the overall control unit 24 obtains the bit state from each of the search units 10a1 to 10aN and obtains the solution to the optimization problem. The overall control unit 24 outputs an end signal indicating the end of computation. The termination signal may contain information indicative of the solution obtained by the computation. For example, the overall control unit 24 outputs image information indicating the solution to a display device connected to the optimization device 1, and causes the display device to display the image information indicating the solution, thereby displaying the content of the obtained solution. may be presented to the user.

Next, circuit configurations of the state transition determination circuits 13b1 to 13bn will be described. Although the state transition determination circuit 13b1 will be described below as an example, the other state transition determination circuits have the same circuit configuration.

FIG. 3 is a diagram showing a circuit configuration example of a state transition determination circuit.
State transition determination circuit 13 b 1 has random number generator 111 , threshold generator 112 and comparator 113 .

The random number generator 111 generates a uniform random number u and outputs it to the threshold generator 112 .
The threshold generation unit 112 uses the uniform random _number u and the temperature information indicating the temperature T1 supplied from the temperature control unit 22 to generate the equation (12) (or the equation (13)) according to the aforementioned conversion table. generates a threshold T·f ⁻¹ (u) based on Threshold generation section 112 outputs the generated threshold T·f ⁻¹ (u) to comparison section 113 .

Comparing section 113 compares (−ΔE ₁ +E _off ) output from adder 13a1 with threshold value T·f ⁻¹ (u), and outputs a flag indicating whether transition is possible or not to selector section 13c. As described above, for example, when (−ΔE ₁ +E _off )≧T·f ⁻¹ (u), the comparison unit 113 outputs a transition permitted signal to the selector unit 13c. The state transition determination circuit 13b1 outputs a transition impossibility to the selector section 13c when (−ΔE ₁ +E _off )<T·f ⁻¹ (u).

Next, a circuit configuration example of the selector section 13c will be described.
FIG. 4 is a diagram showing a circuit configuration example of a selector unit.
The selector unit 13c has a plurality of selection circuits and random number bit generators 32a, 32b, 32c, . Random number bit generators 32a to 32r are provided for each stage of a plurality of selection circuits connected in a tree. Each of the random number bit generators 32a to 32r generates a 1-bit random number having a value of 0 or 1 and supplies it to the selection circuit at each stage. A 1-bit random number is used to select one of the pairs of input flags.

Each of the selection circuits 31a1, 31a2, 31a3, 31a4, . For example, a pair of a flag output by the first state transition determination circuit 13b1 and a flag output by the second state transition determination circuit 13b2 is input to the selection circuit 31a1. A pair of a flag output by the third state transition determination circuit and a flag output by the fourth state transition determination circuit is input to the selection circuit 31a2. Thereafter, similarly, a pair of a flag output by the (n-1)th state transition determination circuit and a flag output by the nth state transition determination circuit 13bn is input to the selection circuit 31ap. In this way, pairs of flags output by adjacent state transition determination circuits are input to the first-stage selection circuit. The number of selection circuits 32a1 to 31ap in the first stage is n/2. After that, the number of selection circuits is halved for each stage.

Each of the selection circuits 31a1 to 31ap selects one of the input pair of flags based on the input pair of flags and the 1-bit random number output from the random number bit generator 32a. Each of the selection circuits 31a1-31ap outputs a state signal including the selected flag and a 1-bit identification value corresponding to the selected flag to the second-stage selection circuits 31b1-31bq. For example, the state signal output by the selection circuit 31a1 and the state signal output by the selection circuit 31a2 are input to the selection circuit 31b1. Similarly, pairs of status signals output by adjacent selection circuits among the selection circuits 31a1 to 31ap are input to the second-stage selection circuit.

Each of the selection circuits 31b1 to 31bq selects one of the input state signals based on the pair of input state signals and the 1-bit random number output from the random number bit generator 32b. Each of the selection circuits 31b1 to 31bq outputs a selected state signal to the selection circuits 31c1, . . . of the third stage. Here, the selection circuits 31b1 to 31bq update the state signal included in the selected state signal by adding 1 bit to indicate which state signal is selected, and output the selected state signal. do.

The same processing is performed in the selection circuits of the third and subsequent stages, and the bit width of the identification value is increased by one bit in the selection circuits of each stage. A status signal is output. The identification value included in the state signal output by the selector section 13c corresponds to the index expressed in binary. However, in the circuit configuration example shown in FIG. A value obtained by adding 1 to the identification value output from the selection circuit 31r corresponds to j shown in FIG.

For example, FIG. 4 shows a circuit configuration example of the selection circuit 31bq. Other selection circuits in the second and subsequent stages are also realized by a circuit configuration similar to that of the selection circuit 31bq.
Inputs of the selection circuit 31bq are a first status signal (status_1) and a second status signal (status_2). The output of the selection circuit 31b1 is a status signal (status). Select circuit 31bq has an OR circuit 131, a NAND circuit 132 and selectors 133 and 134. FIG.

The flag (flag1) included in the status signal (status_1) and the flag (flag2) included in the status signal (status_2) are input to the OR circuit 131 . For example, the status signal (status_1) is the output of the upper side (larger index side) of the two preceding stage selection circuits, and the status signal (status_2) is the lower side (smaller index side) of the two preceding stage selection circuits. ) is the output. The OR circuit 131 outputs the OR operation result (flag) of flag1 and flag2.

Flag1 and flag2 are input to the NAND circuit 132 . The NAND circuit 132 outputs the NAND operation result of flag1 and flag2 to the selection signal input terminal of the selector 133 .

Flag1 and a 1-bit random number (rand) are input to the selector 133 . The selector 133 selects and outputs either flag1 or rand based on the NAND operation result input from the NAND circuit 132 . For example, the selector 133 selects flag1 when the NAND operation result of the NAND circuit 132 is "1", and selects rand when the NAND operation result of the NAND circuit 132 is "0".

The selector 134 receives the index1 included in the status signal (status_1) and the index2 included in the status signal (status_2). A selection signal input terminal of the selector 134 receives a selection result of the selector 133 . The selector 134 selects and outputs either index1 or index2 based on the selection result of the selector 133 . For example, the selector 134 selects index1 when the selection result of the selector 133 is "1", and selects index2 when the selection result of the selector 133 is "0".

A set of outputs from the OR circuit 131 and the selectors 133 and 134 forms a status signal (status) output from the selection circuit 31bq.
Note that the input of the selection circuit in the first stage does not include the identification value. Therefore, the selection circuit in the first stage adds the bit value corresponding to the selected one ("0" for the lower side and "1" for the upper side) as the identification value (indicated as index in the figure). and output the circuit.

In this manner, the selector unit 13c selects one spin bit from transitionable spin bits in a tournament manner. Each match of the tournament (ie, selection in each selection circuit) adds the winning (ie, selected) entry number (0 or 1) to the high-order bits of the index word. The index output by the final-stage selection circuit 31r indicates the selected spin bit. For example, when the number of spin bits in one search unit is 1024, the state signal output from the final-stage selection circuit 31r includes a flag indicating whether transition is possible or not, and an index represented by 10 bits.

However, as an index output method, a method other than the method of generating by the selector unit 13c as described above is conceivable. For example, the index corresponding to each state transition determination circuit is supplied from each of the state transition determination circuits 13b1 to 13bn to the selector unit 13c, and the selector unit 13c selects a flag indicating whether or not the transition is possible and the index corresponding to the flag. good too. In this case, each of the state transition determination circuits 13b1 to 13bn further has an index register for storing the index corresponding to itself, and supplies the index from the index register to the selector section 13c.

FIG. 5 is a diagram illustrating a circuit configuration example of a temperature adjustment unit.
The temperature adjustment section 21 has a register 210 , a minimum energy update confirmation circuit 220 , a maximum temperature update confirmation circuit 230 , a temperature histogram calculation circuit 240 and a temperature calculation circuit 250 .

The register 210 stores the lowest energy reached and the highest set temperature (maximum temperature) in association with each of the search units 10a1 to 10aN.
Minimum energy update confirmation circuit 220 receives energy value E from each of search units 10a1 to 10aN at a predetermined data acquisition timing. The minimum energy update confirmation circuit 220 compares the received energy value E for each search unit with the minimum energy for each search unit stored in the register 210, thereby confirming whether or not the minimum energy has been updated for each search unit. Confirm. The minimum energy update confirmation circuit 220 outputs to the maximum temperature update confirmation circuit 230 and the temperature histogram calculation circuit 240 a signal indicating whether or not the minimum energy has been updated for each search unit. When the minimum energy is updated in a certain search unit, the minimum energy update confirmation circuit 220 updates the minimum energy of the search unit recorded in the register 210 to the energy obtained this time from the search unit.

The maximum temperature update confirmation circuit 230 stores the temperature supplied from the temperature control unit 22 in the register 210 when the confirmation result by the minimum energy update confirmation circuit 220 indicates that the minimum energy has not been updated for a certain search unit. It compares with the maximum temperature of the corresponding search part that was obtained. The maximum temperature update confirmation circuit 230 confirms whether or not the maximum temperature of the relevant search unit has been updated since the previous minimum energy update, according to the comparison. When the maximum temperature is updated, the maximum temperature update confirmation circuit 230 updates the maximum temperature information recorded in the register 210 with the temperature set in the corresponding search section.

When the confirmation result by the minimum energy update confirmation circuit 220 indicates that the minimum energy has been updated for a certain search section, the temperature histogram calculation circuit 240 calculates the maximum temperature of the corresponding search section stored in the register 210 as Count on the temperature histogram. One temperature histogram is generated for all of the search units 10a1 to 10aN.

Based on the temperature histogram generated by the temperature histogram calculation circuit 240, the temperature calculation circuit 250 calculates N new temperatures to be set in the search units 10a1 to 10aN. Temperature calculation circuit 250 uses equations (6) and (7) to calculate the new temperature. Minimum temperature tmp_min is preset in temperature calculation circuit 250 . The maximum temperature tmp_max is determined by the temperature calculation circuit 250 based on the temperature histogram. The temperature calculation circuit 250 can be externally input with a predetermined coefficient α used to calculate a new temperature. The temperature calculation circuit 250 outputs new temperature information indicating the calculated new temperature and a temperature setting signal (T set sig.) to the temperature controller 22 .

FIG. 6 is a diagram showing an example of data stored in a register.
Each address of the register 210 is associated with one of the search units, and data related to the search unit is stored. For example, the address "0xXXXXXXX00" of the register 210 is associated with the search unit 10a1, and the lowest energy reached by the search unit 10a1 is stored at this address. For example, the lowest energy is represented with a width of 128 bits. Thereafter, similarly, the lowest energy for each search section is stored in the register 210 for each 128-bit width, for example, the lowest energy for the second search section 10a2, the lowest energy for the third search section, and so on.

Further, the address "0xXXXXXXY0" of the register 210 is associated with the search unit 10a1, and the highest temperature set in the search unit 10a1 since the previous minimum energy update in the search unit 10a1 is stored at this address. be. For example, temperature is represented with a 32-bit width. Thereafter, similarly, the temperature information of the second search unit 10a2, the temperature information of the third search unit, and so on are set for each 32-bit width, for example, from the last update of the minimum energy for each search unit. The highest temperature is stored in register 210 .

In the above configuration example, the temperature adjustment unit 21 is realized using a dedicated electronic circuit, but the function of the temperature adjustment unit 21 is realized by software processing executed by a processor such as a CPU (Central Processing Unit). can also Therefore, an example of an algorithm for data acquisition by the temperature adjustment unit 21 will be described.

FIG. 7 is a diagram showing an example of a data acquisition algorithm.
Code C1 shows the definition of the variables.
min_eg indicates the energy obtained at the data acquisition timing.

min_eg_pre indicates the lowest energy up to now.
tmp_idx indicates the current temperature value (or the temperature index corresponding to the temperature). For the temperature index, the higher the number, the higher the temperature.

tmp_idx_pre indicates the highest temperature value in the past. "Past" for tmp_idx_pre indicates the period from the last update of the lowest energy to the present.

histogram indicates a temperature histogram (temperature histogram).
Variables min_eg, min_eg_pre, tmp_idx, and tmp_idx_pre are provided for each search unit. There is one histogram for each of the search units 10a1 to 10aN.

Code C2 indicates an algorithm of the temperature adjustment section 21 written using the variables defined by Code C1. Code C2 is executed repeatedly or in parallel for each search unit.
The first line determines min_eg<min_eg_pre. That is, the first line is a determination as to whether or not the minimum energy has been updated. If min_eg<min_eg_pre, the 2nd to 4th lines are executed in order, and the process ends. If min_eg≧min_eg_pre, line 6 is executed.

Line 2 adds the frequency of tmp_idx_pre to the temperature histogram (the frequency of tmp_idx_pre is incremented by 1).
In line 3, min_eg_pre is set to the value of min_eg. That is, the lowest energy so far is updated.

In line 4, tmp_idx_pre is set to the value of tmp_idx. That is, tmp_idx_pre is reset to the temperature index when the lowest energy was updated.

Line 6 determines tmp_idx>tmp_idx_pre. That is, the sixth line is a determination as to whether or not the past maximum temperature value has been updated. If tmp_idx>tmp_idx_pre, line 7 is executed. If tmp_idx≤tmp_idx_pre, the process ends.

In line 7, tmp_idx_pre is set to the value of tmp_idx. That is, tmp_idx_pre is updated to the current temperature set for the corresponding search unit.

FIG. 8 is a diagram showing an example of changes in minimum energy and temperature.
A graph 70 shows an example of minimum energy variation in a certain search section. A graph 71 shows an example of temperature change in the search unit.

The horizontal axis of the graphs 70 and 71 is time, and the direction from left to right is the positive direction of time. The same position on the horizontal axis of graphs 70 and 71 indicates the same time. The vertical axis of graph 70 is energy. The vertical axis of the graph 71 is temperature. The vertical axis of graph 71 indicates temperatures Ta, Tb, Tc, and Td. Here, Ta>Tb>Tc>Td.

Graph 70 includes series 70a. According to the series 70a, the minimum energy is updated in two periods 70b and 70c.
Graph 71 includes series 71a. According to the sequence 71a, Ta is the maximum temperature reached by the corresponding search unit between the time when the minimum energy is updated in the period 70b and the time when the minimum energy is updated in the period 70c.

The examples of the graphs 70 and 71 indicate that it is necessary to once increase the temperature to the maximum temperature Ta in order to update the minimum energy in the corresponding search section. Therefore, the temperature adjustment unit 21 acquires the maximum temperature reached for updating the minimum energy as statistical information, and determines the temperature to be set for each search unit based on the statistical information.

FIG. 9 is a diagram showing an example of a temperature histogram.
Temperature histogram 80 is generated by temperature histogram calculation circuit 240 . Further, when the temperature is adjusted using a processor such as a CPU, the temperature histogram 80 corresponds to "histogram" in FIG.

The horizontal axis of the temperature histogram 80 indicates temperature index and the vertical axis indicates frequency.
For example, the temperature calculation circuit 250 determines the temperature corresponding to the temperature index with the highest frequency in the temperature histogram 80 as the maximum temperature tmp_max. Specifically, the temperature calculation circuit 250 determines the maximum temperature tmp_max from among the temperatures with the highest frequencies in the temperature histogram 80 . In one example, the temperature calculation circuit 250 determines the highest frequency temperature indicated by peak p1 as the maximum temperature tmp_max. Note that, when the temperature histogram 80 is created for the temperature index, the temperature calculation circuit 250 identifies the temperature value corresponding to the temperature index by referring to the above-described first correspondence information, for example. In this case, for example, the first correspondence information held by the temperature controller 22 can be referenced by the temperature calculation circuit 250 . The temperature calculation circuit 250 calculates a new temperature tmp[i] (1≤i≤N) from equations (6) and (7) using the determined maximum temperature tmp_max.

However, depending on the problem, the above peak p1 may not appear or multiple peaks may appear. In such a case, for example, temperature calculation circuit 250 uses a cumulative histogram based on temperature histogram 80 to determine maximum temperature tmp_max as follows.

FIG. 10 is a diagram showing an example of a cumulative histogram.
A cumulative histogram 81 is a histogram obtained by accumulating the frequencies shown in the temperature histogram 80 from the lowest temperature. Cumulative histogram 81 is generated by temperature calculation circuit 250 . The horizontal axis of the cumulative histogram 81 indicates the temperature index, and the vertical axis indicates the cumulative frequency.

The temperature calculation circuit 250 determines the maximum temperature tmp_max from the cumulative histogram ratio (cumulative ratio). For example, let the cumulative ratio be 70% (coefficient α=0.7). A cumulative histogram 81 shows a straight line 82 indicating a cumulative percentage of 70%. In this case, the temperature calculation circuit 250 specifies the temperature corresponding to the cumulative frequency obtained by multiplying the maximum value of the cumulative frequency in the cumulative histogram 81 by the coefficient α indicating the cumulative ratio (the temperature corresponding to the cumulative frequency of the point p2), Determine the temperature as the maximum temperature tmp_max. In this example, the maximum cumulative frequency is the cumulative frequency corresponding to the maximum temperature index. The maximum cumulative frequency corresponds to the total number of times the minimum energy of each search unit has been updated.

The temperature calculation circuit 250 calculates a new temperature tmp[i] (1≤i≤N) from equations (6) and (7) using the determined maximum temperature tmp_max. Note that the coefficient α used as the cumulative ratio may be input from the outside as described above.

As described above, temperature calculation circuit 250 may use cumulative histogram 81 to determine maximum temperature tmp_max when peak p1 is not detected in temperature histogram 80, or when multiple peaks are detected. Alternatively, whether to use the temperature histogram 80 or the cumulative histogram 81 may be preset in the temperature calculation circuit 250 .

Next, a processing procedure by the optimization device 1 will be described.
FIG. 11 is a flowchart showing an example of overall control of replica exchange.
(S1) The overall control unit 24 receives temperature information indicating an initial temperature as input data from the outside, and outputs a start signal to the temperature control unit 22 together with the temperature information.

(S2) The temperature control unit 22 receives the activation signal from the overall control unit 24, and outputs temperature information and a temperature setting signal to each of the search units 10a1 to 10aN to set the temperature. 10aN to perform a probabilistic search process. The details of the processing (search processing) by each of the search units 10a1 to 10aN will be described later.

(S3) When each of the search units 10a1 to 10aN executes the stochastic search for a specified time or a specified number of iterations, the temperature adjustment unit 21 adjusts the energy value calculated by each of the search units 10a1 to 10aN. Data collection processing including acquisition of Details of the data collection process will be described later.

(S4) The search units 10a1 to 10aN transmit the energy value of each adjacent search unit to the temperature control unit 22. The temperature control unit 22 acquires the energy values calculated by the search units 10a1 to 10aN for each search unit having adjacent temperatures.

(S5) The exchange control unit 23 performs temperature exchange control based on the exchange probability based on the formula (5) using the energy difference between the search units with adjacent temperatures. The exchange control unit 23 performs temperature exchange control for each pair of search units having adjacent temperatures. The details of exchange control will be described later.

(S6) The temperature adjustment unit 21 determines whether it is within the data acquisition period for temperature adjustment. If it is within the data acquisition period for temperature adjustment, the process proceeds to step S2. If it is not within the data acquisition period for temperature adjustment, the process proceeds to step S7.

(S7) Based on the temperature histogram 80 (or cumulative histogram 81) generated as a result of the data collection process in step S3, the temperature adjustment unit 21 calculates the maximum temperature tmp_max used in equations (6) and (7). do. The temperature adjustment unit 21 uses the calculated maximum temperature tmp_max to calculate a new temperature tmp[i] based on equations (6) and (7). The temperature adjustment unit 21 outputs new temperature information indicating the calculated new temperature and a temperature setting signal to the temperature control unit 22 . The temperature control unit 22 receives the new temperature information and the temperature setting signal output by the temperature adjustment unit 21, and determines the temperature associated with each temperature index in the first correspondence information held by the temperature control unit 22. Update.

(S8) The temperature control unit 22 outputs the new temperature information and the temperature setting signal to each of the search units 10a1 to 10aN to set the temperature, and the probabilistic search (ground state search) by each of the search units 10a1 to 10aN. ) is executed.

(S9) The search units 10a1 to 10aN transmit the energy value of each adjacent search unit to the exchange control unit 23 when the search units 10a1 to 10aN execute the probabilistic search for a specified time or a specified number of iterations. do. The exchange control unit 23 acquires the energy values calculated by the search units 10a1 to 10aN for each search unit having adjacent temperatures.

(S10) The exchange control unit 23 performs temperature exchange control based on the exchange probability based on the formula (5) using the energy difference between the search units with adjacent temperatures. The exchange control unit 23 performs temperature exchange control for each pair of search units having adjacent temperatures.

(S11) The search units 10a1 to 10aN determine whether or not there is no change in the bit state in the minimum temperature search units specified times. When there is no change in the bit state in the search unit with the lowest temperature, the search units 10a1 to 10aN output the bit state to the general control unit 24, and complete the overall control process of replica exchange. If there is a change in the bit state in the lowest temperature search unit, the search units 10a1 to 10aN advance the process to step S8 to continue the stochastic search process.

FIG. 12 is a flowchart illustrating an example of processing by the search unit.
The search unit process corresponds to steps S2 and S8.
(S20) The temperature control unit 22 sets the temperature for each of the searching units 10a1 to 10aN. For example, the temperature control unit 22 controls the search unit 10a1 based on the first correspondence information that associates the temperature index with the temperature and the second correspondence information that associates the temperature index with the identification information of the search unit. Set the temperature to each of ~10 aN. Alternatively, the temperature control unit 22 may set the temperature for each of the search units 10a1 to 10aN based on the correspondence information that associates the identification information of the search units with the temperatures, as described above. Note that the initial temperature values set in each of the search units 10a1 to 10aN are determined in advance according to the problem or the like.

(S21) Each of the search units 10a1 to 10aN calculates a local field h for each spin bit. For example, focusing on the search unit 10a1, the h calculation units 12b1 to 12bn calculate local fields h ₁ to h _n . The local field h is calculated based on equation (10). After the local field h is calculated by Equation (10), the updated local field h=h+δh can be obtained by, for example, adding the difference δh shown by Equation (11) to the local field h. can.

(S22) Each of the search units 10a1 to 10aN calculates an energy change value ΔE for each spin bit based on the calculated local field h. For example, focusing on the searching unit 10a1, the ΔE generating units 12c1 to 12cn calculate energy change values ΔE1 to ΔEn. ΔE is calculated based on equation (9).

(S23) Each of the search units 10a1 to 10aN adds the offset value _Eoff to the energy change value -ΔE. For example, focusing on the search unit 10a1, the adders 13a1 to 13an add the offset value E _off to -ΔE ₁ to -ΔE _n . The offset value _Eoff is controlled by the offset controller 13d as described above. For example, the offset control unit 13d supplies an offset value E _off greater than 0 to the adders 13a1 to 13an when the flag indicating whether transition is possible or not output by the selector unit 13c indicates that the transition is not possible. The offset control unit 13d supplies the offset value E _off =0 to the adders 13a1 to 13an when the flag indicates that the transition is permitted. Note that the initial value of the offset value _Eoff is zero.

(S24) Each of the searching units 10a1 to 10aN selects a spin bit to be inverted among the spin bits of the inversion candidates. For example, focusing on the search unit 10a1, each of the state transition determination circuits 13b1 to 13bn outputs to the selector unit 13c a flag indicating whether or not the spin bit corresponding to the corresponding state transition determination circuit can be transitioned. The selector unit 13c selects one of the input flags and outputs the selected flag and an index indicating the spin bit corresponding to the selected flag.

(S25) Each of the search units 10a1 to 10aN inverts the selected spin (spin bit). For example, focusing on the searching unit 10a1, the state holding unit 11 determines the value of the spin bit indicated by the index among the spin bits included in the bit state based on the flag output by the selector unit 13c and the index. Update.

(S26) Each of the search units 10a1 to 10aN determines whether or not a specified number of iterations has been reached or a specified time has elapsed since the start of the probabilistic search immediately after step S20. If the prescribed number of iterations has been reached or the prescribed time has elapsed, the process proceeds to step S27. If the prescribed number of iterations has not been reached and the prescribed time has not elapsed, the process proceeds to step S21.

(S27) Each of the search units 10a1 to 10aN calculates the energy value (E ₁ to E _N ) in the corresponding search unit and outputs it to the temperature adjustment unit 21 and the temperature control unit 22.
As described above, each of the search units 10a1 to 10aN accepts one of a plurality of state transitions according to the relative relationship between the change value and the thermal excitation energy based on the temperature value, the change value of the energy, and the random value. Probabilistically determine whether or not At the time of the determination, each transition control unit (for example, transition control unit 13) of search units 10a1 to 10aN adds a predetermined offset value to the change value of the energy value. This facilitates the escape from the local solution and speeds up the computation.

FIG. 13 is a flowchart illustrating an example of data collection processing.
The data collection process corresponds to step S3. Although the procedure for the search unit 10a1 by the temperature adjustment unit 21 will be described below, the same procedure is applied to the search units 10a2 to 10aN. Steps S31 to S34 below are executed for each of the search units 10a1 to 10aN. One temperature histogram 80 in step S34 is calculated for each of the search units 10a1 to 10aN.

(S30) The minimum energy update confirmation circuit 220 determines whether or not it is time to collect data. If it is the data collection timing, the process proceeds to step S31. If it is not the data collection timing, the data collection process ends. Here, the data collection timing may be the timing each time the search processing (procedure in FIG. 12) of the search units 10a1 to 10aN is completed, or the timing each time the search processing is completed a plurality of times. The data collection timing is set in advance for the temperature adjustment unit 21 .

(S31) _The minimum energy update confirmation circuit 220 acquires the energy E1 from the search section 10a1. _The minimum energy update confirmation circuit 220 compares the minimum energy of the searching unit 10a1 stored in the register 210 with the obtained energy E1, and determines whether or not the minimum energy has been updated. A case where the minimum energy of the searching section 10a1 is updated is _a case where the energy E1 acquired from the searching section 10a1 is lower than the lowest energy of the searching section 10a1 stored in the register 210. FIG. When the minimum energy is updated, the minimum energy update confirmation circuit 220 updates the record of the minimum energy of the searching unit _10a1 stored in the register 210 to the energy E1 obtained this time from the searching unit 10a1, and proceeds to step S34. Processing proceeds. If the minimum energy has not been updated, the process proceeds to step S32.

(S32) The maximum temperature update confirmation circuit 230 acquires the temperature set in the search unit 10a1 from the temperature control unit 22, and determines whether or not the maximum temperature for the search unit 10a1 stored in the register 210 has been updated. do. A case where the maximum temperature of search section 10a1 is updated is a case where the temperature set in search section 10a1 is higher than the maximum temperature stored in register 210 for search section 10a1. If the maximum temperature has been updated, the process proceeds to step S33. If the maximum temperature has not been updated, the data collection process for the search unit 10a1 ends.

(S33) The maximum temperature update confirmation circuit 230 updates the record of the maximum temperature of the search unit 10a1 stored in the register 210 to the temperature currently set in the search unit 10a1 obtained from the temperature control unit 22. Then, the data collection process for the search unit 10a1 ends.

(S34) The temperature histogram calculation circuit 240 reads out the maximum temperature corresponding to the search unit 10a1 from the register 210, and adds 1 to the frequency (frequency) of the maximum temperature in the temperature histogram 80. As described above, one temperature histogram 80 is generated for each of the search units 10a1 to 10aN. Also, the maximum temperature update confirmation circuit 230 updates the record of the maximum temperature of the search unit 10a1 stored in the register 210 to the temperature currently set in the search unit 10a1 obtained from the temperature control unit 22. FIG. Then, the data collection process for the search unit 10a1 ends.

Note that the temperature adjustment unit 21 may execute the processing of steps S31 to S34 in parallel for each of the search units 10a1 to 10aN. Alternatively, the temperature adjusting section 21 may sequentially select one of the searching sections 10a1 to 10aN and repeat the processes of steps S31 to S34.

FIG. 14 is a flowchart showing an example of exchange control.
Exchange control corresponds to steps S5 and S10.
(S40) The exchange control unit 23 determines whether or not to exchange the temperature with the adjacent higher (or lower) temperature search unit for the even-numbered search unit, based on the exchange probability shown in equation (5). do. The determination of temperature exchange is performed for each pair of search units. The function f of the equation (5) uses the function of the Metropolis method of the equation (2) or the function of the Gibbs method of the equation (3). If there is a pair of search units determined to exchange temperatures, the process proceeds to step S41. If there is no pair of search units determined to exchange temperatures, the process proceeds to step S42.

(S41) The exchange control unit 23 exchanges temperatures for the pair of search units determined to exchange temperatures in step S40. The exchange control unit 23 updates the above-described second correspondence information held by the exchange control unit 23 according to the temperature exchange.

(S42) The exchange control unit 23 determines whether or not to exchange the temperature with an adjacent higher (or lower) temperature search unit for the odd-numbered search units, based on the exchange probability shown in Equation (5). do. The determination of temperature exchange is performed for each pair of search units. The function f of the equation (5) uses the function of the Metropolis method of the equation (2) or the function of the Gibbs method of the equation (3). If the exchange control unit 23 determines in step S40 whether or not to exchange the temperature of the even-numbered search unit with the higher temperature search unit, in step S42, the odd-numbered search unit of the higher temperature. determines whether to exchange the temperature with When the exchange control unit 23 determines in step S40 whether or not to exchange the temperature of the even-numbered search unit with the lower temperature search unit, in step S42, the temperature of the odd-numbered search unit is changed to the lower temperature search unit. determines whether or not to replace the If there is a pair of search units determined to exchange temperatures, the process proceeds to step S43. If there is no pair of search units determined to exchange temperatures, the exchange control ends.

(S43) The exchange control unit 23 exchanges temperatures for the pair of search units determined to exchange temperatures in step S42. The exchange control unit 23 updates the second correspondence information held by the exchange control unit 23 according to the temperature exchange. Then, the exchange control ends.

In the above example, the temperature exchange control is performed by focusing on the odd-numbered search unit next to the even-numbered search unit. You may pay attention and perform exchange control of temperature. That is, steps S40 and S41 may be executed after steps S42 and S43.

Next, an example of the flow of processing by the optimization device 1 will be described. Below, the case where temperature adjustment is performed by software processing by the CPU and the case where temperature adjustment is performed by hardware processing indicated by the temperature adjustment unit 21 will be exemplified.

First, a case where temperature adjustment is performed by software processing by a CPU will be exemplified. In this case, for example, the function of the temperature adjustment unit 21 is implemented in the optimization device 1 as a function of software executed by the CPU. Also, the functions of the temperature control unit 22 (including the exchange control unit 23) are implemented in the optimization device 1 not only as hardware, but also as software functions executed by the CPU. Steps S3 to S7 in FIG. 11 are executed as software processing executed by the CPU, and steps S2 and S8 to S11 in FIG. 11 are executed as hardware processing.

FIG. 15 is a diagram illustrating an example (part 1) of the flow of processing.
The horizontal axis in FIG. 15 indicates the number of iterations (or time), and the direction from left to right is the positive direction.

The data acquisition period by the CPU includes periods t11, t12, t13, and t14 in units of HW (Hardware) activation. The HW activation unit period is a unit period during which the search units 10a1 to 10aN are activated to execute the search process (base state search). The period (core interval) during which the probabilistic search is performed after temperature adjustment includes the period t15 in units of HW activation. In the figure, the "X" mark indicates the timing of replica exchange (that is, temperature exchange). Data acquisition by the CPU is performed immediately before replica exchange during the data acquisition period.

For example, the CPU acquires the energy (and the temperature if the lowest energy is not updated) in the search units 10a1 to 10aN immediately after the period t11 is completed. The CPU creates a temperature histogram 80 in response to the updated minimum energy. After that, the CPU performs replica exchange (temperature exchange control). Then, the probabilistic search is performed by the search units 10a1 to 10aN in the next period t12. Thus, in the data acquisition period, immediately after each of the periods t11, t12, t13, and t14, the CPU acquires data and creates the temperature histogram 80 for the search units 10a1 to 10aN. Upon completion of the data acquisition period, the CPU determines a new temperature tmp[i] based on temperature histogram 80 . The length of the data acquisition period is set in advance for the software executed by the CPU (for example, when the total number of iterations for stochastic search is determined, it is set to about 1% of the total number of iterations). Such).

The new temperature tmp[i] is then used to start the core interval period t15. In the core interval, the probabilistic search and replica exchange are executed by the search units 10a1 to 10aN and the hardware-implemented temperature control unit 22 (including the exchange control unit 23) without the CPU intervening in the processing. Therefore, the period of the core interval corresponds to the period t15 of the HW activation unit.

In the above example, after the first data acquisition period of the entire period of the stochastic search by the search units 10a1 to 10aN, the stochastic search is executed without changing the adjusted temperature. On the other hand, a data acquisition period may be provided periodically, the CPU repeatedly executes data acquisition and temperature determination based on the acquired data, and changes the temperatures set in the search units 10a1 to 10aN each time.

Next, the flow of processing when temperature adjustment is performed by hardware processing will be described.
FIG. 16 is a diagram illustrating an example (2) of the flow of processing.
The horizontal axis in FIG. 16 indicates the number of iterations (or time), and the direction from left to right is the positive direction.

When temperature adjustment is performed by hardware processing, the entire period including the data acquisition period and the core interval is the HW activation unit period.
The data acquisition period by the temperature adjustment unit 21 includes unit periods t21, t22, t23, and t24. A period t25 is a core interval. In the figure, the "X" mark indicates the timing of replica exchange (that is, temperature exchange). Data acquisition by the temperature adjustment unit 21 is performed immediately before replica exchange during the data acquisition period.

For example, the temperature adjuster 21 acquires the energy (and the temperature if the lowest energy is not updated) in the searchers 10a1 to 10aN immediately after the period t21 is completed. The temperature adjuster 21 creates a temperature histogram 80 according to the update of the minimum energy. Thereafter, the exchange control unit 23 performs replica exchange (temperature exchange control). Then, the probabilistic search is performed by the search units 10a1 to 10aN in the next period t22. Thus, in the data acquisition period, immediately after each of the periods t21, t22, t23, and t24, the temperature adjuster 21 acquires data and creates the temperature histogram 80 for the searchers 10a1 to 10aN. When the data acquisition period is completed, the temperature adjuster 21 determines a new temperature tmp[i] based on the temperature histogram 80 .

Note that the length of the data acquisition period is set in advance for the temperature adjustment unit 21 (for example, when the total number of iterations for stochastic search is determined, it is set to about 1% of the total number of iterations, etc.). ). Then, using the new temperature tmp[i], the core interval period t25 is started.

In the above example, after the first data acquisition period of the entire period of the stochastic search by the search units 10a1 to 10aN, the stochastic search is executed without changing the adjusted temperature. On the other hand, a data acquisition period is provided periodically, and the temperature adjustment unit 21 repeatedly executes data acquisition and temperature determination based on the acquired data, and changes the temperatures set in the search units 10a1 to 10aN each time. good.

According to the optimization device 1, the temperatures to be set in the search units 10a1 to 10aN can be appropriately determined. Specifically, the maximum value of the new temperature tmp[i] is determined based on the update of the minimum energy in the data acquisition period and the statistical information of the set maximum temperature, and the temperature set for each search unit can be prevented from being too high or too low. Therefore, the solution accuracy in the optimization device 1 can be improved. In addition, by improving the solution accuracy, it is possible to increase the possibility of reaching an appropriate solution more quickly, and to speed up the calculation.

Also, in order to determine an appropriate maximum temperature (temperature corresponding to tmp_max), it is conceivable that the optimization process by the optimization device 1 is repeatedly executed and the user manually adjusts. It takes a lot of work. On the other hand, by determining the maximum temperature tmp_max based on the temperature statistical information as described above, it is possible to reduce the trouble of temperature adjustment by the user.

When the temperature adjustment is performed by hardware processing, the overhead associated with data output to and input from the CPU can be reduced compared to when the temperature adjustment is performed by software processing, thereby speeding up the calculation.

Here, as the hardware configuration of the optimization device 1, the following example is also conceivable.
FIG. 17 is a diagram showing another hardware example of the optimization device.
The optimization device 1a includes a CPU 101, a RAM (Random Access Memory) 102, a HDD (Hard Disk Drive) 103, a NIC (Network Interface Card) 104, an output IF (Interface) 105, an input IF 106, a medium reader 107, and a probabilistic search unit. 108.

The CPU 101 is a processor that executes program instructions. The CPU 101 loads at least part of the programs and data stored in the HDD 103 into the RAM 102 and executes the programs. Note that the CPU 101 may include multiple processor cores. Also, the optimization device 1a may have a plurality of processors. A collection of multiple processors is sometimes called a "multiprocessor" or simply a "processor." The CPU 101 can function as an overall control unit 24, for example. Further, as described above, the functions of the control unit 20 (that is, the temperature adjustment unit 21, the temperature control unit 22, and the replacement control unit 23) can be realized by processing software (control program) executed by the CPU 101.

The RAM 102 is a volatile semiconductor memory that temporarily stores programs executed by the CPU 101 and data used by the CPU 101 for calculation. Note that the optimization device 1a may be provided with a type of memory other than the RAM, and may be provided with a plurality of memories.

The HDD 103 is a nonvolatile storage device that stores an OS (Operating System), software programs such as middleware and application software, and data. Note that the optimization device 1a may include other types of storage devices such as flash memory and SSD (Solid State Drive), or may include a plurality of nonvolatile storage devices.

The NIC 104 is an interface that is connected to the network 40 and communicates with other computers via the network 40 . The NIC 104 is, for example, connected to a communication device such as a switch or router by a cable.

The output IF 105 outputs an image to the display 41 connected to the optimization device 1a according to instructions from the CPU 101 . As the display 41, any type of display can be used, such as a CRT (Cathode Ray Tube) display, a liquid crystal display (LCD: Liquid Crystal Display), a plasma display, or an organic EL (OEL: Organic Electro-Luminescence) display.

The input IF 106 acquires an input signal from the input device 42 connected to the optimization device 1 a and outputs it to the CPU 101 . As the input device 42, a pointing device such as a mouse, a touch panel, a touch pad, or a trackball, a keyboard, a remote controller, a button switch, or the like can be used. Moreover, a plurality of types of input devices may be connected to the optimization apparatus 1a.

The medium reader 107 is a reading device that reads programs and data recorded on the recording medium 43 . As the recording medium 43, for example, a magnetic disk, an optical disk, a magneto-optical disk (MO), a semiconductor memory, or the like can be used. Magnetic disks include flexible disks (FDs) and HDDs. Optical discs include CDs (Compact Discs) and DVDs (Digital Versatile Discs).

The medium reader 107 copies, for example, programs and data read from the recording medium 43 to other recording media such as the RAM 102 and the HDD 103 . The read program is executed by the CPU 101, for example. Note that the recording medium 43 may be a portable recording medium, and may be used for distribution of programs and data. Also, the recording medium 43 and the HDD 103 may be referred to as a computer-readable recording medium.

The probabilistic search unit 108 is an accelerator that uses hardware to perform computations for combinatorial optimization problems by the method of replica exchange. The probabilistic search unit 108 has search units 10a1 to 10aN, a temperature adjustment unit 21, a temperature control unit 22, and an exchange control unit 23, and searches for the ground state of the Ising model according to the procedures in FIGS. 11 to 14 described above. Perform a probabilistic search.

Functions similar to those of the optimization device 1 can be realized by the optimization device 1a.
[Second embodiment]
Next, a second embodiment will be described.

The second embodiment differs from the configuration shown in FIG. 2 and subsequent figures described in the first embodiment in that the values of a plurality of state variables (spin bit strings) are exchanged in the search units 10a1 to 10aN. In the second embodiment, the temperatures set in the search units 10a1 to 10aN are constant unless temperature adjustment is performed. For example, the temperatures are set in ascending order or descending order for the search units 10a1 to 10aN.

FIG. 18 is a diagram illustrating a circuit configuration example of an optimization device according to the second embodiment.
The optimization device 2 is implemented using, for example, a semiconductor integrated circuit such as FPGA. The optimization device 2 has search units 10a1 to 10aN, a temperature adjustment unit 21a, a state control unit 23a, and an overall control unit 24a.

The search units 10a1 to 10aN have the same circuit configuration as the search units 10a1 to 10aN exemplified in FIG. 2, so description thereof will be omitted.
However, in the second embodiment, the bit state (spin bit string) and the replica number, which is the bit state identification information, are set by the state control unit 23a to the state holding unit of each search unit. Since the number of search units 10a1 to 10aN is N, the total number of bit states in the optimization device 2 is also N. Also, a local field is set by the state control unit 23a for the h calculation unit of each search unit.

Also, the E calculator of each search unit outputs the energy E to the temperature adjuster 21a and the state controller 23a. The E calculator of each search unit outputs the energy E and the replica number set in each search unit to the temperature adjustment unit 21a. For example, FIG. 18 illustrates a case where the replica number “rep_1” is output from the searching unit 10a1, the replica number “rep_2” is output from the searching unit 10a2, and the replica number “rep_N” is output from the searching unit 10aN. there is

Furthermore, the state holding unit 11 outputs the bit state and the local field (sometimes abbreviated as LF (Local Field) in the figure) set in the h calculation units 12b1 to 12bn to the state control unit 23a. do.

Temperature adjustment unit 21a receives energy values and replica numbers output from search units 10a1 to 10aN. The temperature adjuster 21a obtains the temperature set in each of the searchers 10a1 to 10aN. FIG. 18 shows an example in which the temperature T ₁ is set for the searching unit 10a1, the temperature T ₂ is set for the searching unit 10a2, . . . , and the temperature _TN is set for the searching unit 10aN. The temperature adjuster 21a determines new temperature information indicating a new temperature to be set in each of the searchers 10a1 to 10aN in accordance with the change in energy value and the change in temperature corresponding to the bit state. The temperature adjustment unit 21a outputs the determined new temperature information and the new temperature setting signal (T set sig.) to the search units 10a1 to 10aN via a temperature control unit (not shown). The new temperature information is set in the state transition determination circuit (for example, state transition determination circuits 13b1 to 13bn) of each search unit.

The state control unit 23a performs exchange control of states (including bit states and local fields) in the search units 10a1 to 10aN. The state control unit 23 a is an example of the replacement control unit 23 .

The state control unit 23a supplies the bit state and the bit state setting signal (BS set sig.) to the state holding unit of each of the searching units 10a1 to 10aN. The bit state setting signal includes a replica number corresponding to the bit state. Further, the state control unit 23a supplies the local field and the local field setting signal (LF set sig.) to the h calculation unit included in each of the search units 10a1 to 10aN.

The state control unit 23a determines whether or not to exchange states for pairs of two search units having adjacent temperatures, based on the exchange probability of Equation (5). The state control unit 23a supplies the exchanged bit state and local field to each search unit.

For example, the state control unit 23a holds first correspondence information that associates temperature indexes with temperatures in a register of the state control unit 23a. For example, temperature indices are associated with temperatures in ascending order of temperature (the higher the temperature index, the higher the temperature). In the second embodiment, the temperature index is also identification information for the search unit. Further, the state control unit 23a holds, for example, third correspondence information in which temperature indexes arranged in ascending order of temperature are associated with identification numbers (replica numbers) of bit states in a register of the state control unit 23a. do. The state control unit 23a controls state exchange for the search units 10a1 to 10aN based on the first correspondence information and the third correspondence information, and updates the third correspondence information according to the exchange. State exchange may be performed for pairs of search units having adjacent temperature indices in the second correspondence information. The state control unit 23a supplies bit states and local fields to the search units 10a1 to 10aN based on the third correspondence information.

However, the state control unit 23a holds correspondence information in which replica numbers and temperature values (temperature values arranged in ascending order or descending order corresponding to the searching unit) are associated with each other, and state control is performed based on the correspondence information. exchange control may be performed. In that case, the temperature value in the correspondence information is updated according to the calculation result of the new temperature by the temperature adjustment unit 21a.

The overall control unit 24 a controls the overall operation of the optimization device 2 . The overall control unit 24a receives an input of a start signal. Then, the general control unit 24a outputs the initial temperature information and the temperature setting signal (T set sig.) to the search units 10a1 to 10aN, and sets the initial temperature to each of the search units 10a1 to 10aN. Then, the overall control unit 24a outputs a start signal to the state control unit 23a to start the search units 10a1 to 10aN to start calculations for the optimization problem.

After completing the calculation, the overall control unit 24a obtains the bit state from each of the search units 10a1 to 10aN and obtains the solution to the optimization problem. The overall control unit 24a outputs an end signal indicating the end of the computation. The termination signal may contain information indicative of the solution obtained by the computation. For example, the overall control unit 24a outputs image information indicating the solution to a display device connected to the optimization device 2, and causes the display device to display the image information indicating the solution, thereby displaying the content of the obtained solution. may be presented to the user.

FIG. 19 is a diagram illustrating a circuit configuration example of a temperature adjustment unit;
The temperature adjustment unit 21 a has a register 310 , a minimum energy update confirmation circuit 320 , a maximum temperature update confirmation circuit 330 , a temperature histogram calculation circuit 340 and a temperature calculation circuit 350 . The optimization device 2 further has a temperature control section 22a.

The register 310 stores the lowest energy reached and the highest value of the set temperature (maximum temperature) in association with the replica number of each of the N bit states.
Minimum energy update confirmation circuit 320 receives the energy value E and the replica number of the bit state in each search unit from each of search units 10a1 to 10aN at a predetermined data acquisition timing. The minimum energy update confirmation circuit 320 compares the received energy value E for each replica number with the minimum energy for each replica number stored in the register 310, thereby confirming whether or not the minimum energy has been updated for each replica number. to confirm. The minimum energy update confirmation circuit 320 outputs to the maximum temperature update confirmation circuit 330 and the temperature histogram calculation circuit 340 a signal indicating whether or not the minimum energy has been updated for each replica number. The minimum energy update confirmation circuit 320 updates the minimum energy of the replica number recorded in the register 310 to the energy acquired this time for the replica number when the minimum energy is updated in a certain replica number.

Maximum temperature update confirmation circuit 330 updates the current temperature for a certain replica number (bit state) when the result of confirmation by minimum energy update confirmation circuit 320 indicates that the minimum energy has not been updated. It is compared with the maximum temperature of the corresponding replica number stored in register 310 . The maximum temperature update confirmation circuit 330 confirms whether or not the maximum temperature from the previous minimum energy update has been updated by the current set temperature for the replica number in accordance with the comparison. When the maximum temperature is updated, the maximum temperature update confirmation circuit 330 updates the maximum temperature information of the replica number recorded in the register 310 with the current set temperature corresponding to the replica number.

Temperature histogram calculation circuit 340 calculates the maximum temperature of the replica number stored in register 310 when the result of confirmation by minimum energy update confirmation circuit 320 indicates that the minimum energy has been updated for a certain replica number. Count on the temperature histogram. A temperature histogram is generated for all N bit states.

Based on the temperature histogram generated by the temperature histogram calculation circuit 340, the temperature calculation circuit 350 calculates N new temperatures to be set in the search units 10a1 to 10aN. Temperature calculation circuit 350 uses equations (6) and (7) to calculate the new temperature. Minimum temperature tmp_min is preset in temperature calculation circuit 350 . The maximum temperature tmp_max is determined by temperature calculation circuit 350 based on the temperature histogram. The temperature calculation circuit 350 can receive an external input of the coefficient α used to calculate the new temperature. The temperature calculation circuit 350 outputs new temperature information indicating the calculated new temperature and a temperature setting signal (T set sig.) to the temperature control section 22a. Furthermore, the temperature calculation circuit 350 outputs the new temperature information to the state control section 23a to update the temperature associated with the temperature index in the first correspondence information held by the state control section 23a. Note that the temperature calculation method by the temperature calculation circuit 350 is the same as the temperature calculation method by the temperature calculation circuit 250 .

Here, the temperature control unit 22a receives the new temperature information and the temperature setting signal (T set sig.) from the temperature calculation circuit 350. FIG. Then, the temperature control section 22a outputs the new temperature information and the temperature setting signal (T set sig.) to the searching sections 10a1 to 10aN, thereby setting new temperatures for the searching sections 10a1 to 10aN.

Further, when the temperature adjustment unit 21a repeatedly adjusts the temperature at a predetermined cycle or the like during the entire ground state search period, the temperature control unit 22a or the state control unit 23a currently sets each of the search units 10a1 to 10aN. Temperature information may be obtained.

FIG. 20 is a diagram showing an example of data stored in a register.
In register 310, three addresses separated by a predetermined offset are associated with a set of records. For example, addresses "0xXXXXXX00", "0xXXXXXXY0", and "0xXXXXXXZ0" are a set of records corresponding to the replica numbers stored at address "0xXXXXXXZ0". Address "0xXXXXXX00" stores the lowest energy reached by the bit state corresponding to the replica number. For example, the lowest energy is represented with a width of 128 bits. The address "0xXXXXXXY0" stores the highest temperature set in the bitstate of the replica number since the previous minimum energy update. For example, temperature is represented with a 32-bit width. Also, for example, the replica number is represented by a 16-bit width.

Similarly, the minimum energy, temperature, and replica number are stored in register 310 for bit states of other replica numbers.
In this way, the temperature adjustment unit 21a associates the identification information (replica number) of the bit state (plurality of state variables) set in the search unit with the minimum energy value reached for the bit state. , record the maximum temperature set for that bitstate. Then, when the minimum value of the energy value is updated in any of the search units, the temperature adjustment unit 21a changes the bit state ( The highest temperature value among the temperatures set for the plurality of state variables) is acquired as the temperature statistical information.

Next, a processing procedure by the optimization device 2 will be described.
FIG. 21 is a flowchart showing an example of overall control of replica exchange.
(S1a) The overall control unit 24a receives temperature information indicating an initial temperature as input data from the outside, outputs the temperature information to the search units 10a1 to 10aN, and outputs an activation signal to the state control unit 23a.

(S2a) The state control unit 23a receives the activation signal from the general control unit 24a and causes the search units 10a1 to 10aN to execute probabilistic search processing. The processing (search processing) procedure by each of the search units 10a1 to 10aN is the same as the procedure illustrated in FIG.

(S3a) When the search units 10a1 to 10aN execute the probabilistic search for a specified time or a specified number of iterations, the temperature adjustment unit 21a adjusts the energy values and the replica numbers calculated by the search units 10a1 to 10aN. Perform data collection processing including acquisition. Details of the data collection process will be described later.

(S4a) The search units 10a1 to 10aN transmit the energy value, bit state and local field for each adjacent search unit to the state control unit 23a. The state control unit 23a acquires the energy values, bit states, and local fields calculated by the search units 10a1 to 10aN for each pair of adjacent search units. A pair of adjacent search units is a pair of search units whose set temperatures are adjacent to each other. The two bit states in the pair of search units will be adjacent in temperature.

(S5a) The state control unit 23a performs state exchange control based on the exchange probability based on the formula (5) using the energy difference between the search units with adjacent temperatures. The state control unit 23a performs state exchange control for each pair of search units having adjacent temperatures. The details of exchange control will be described later.

(S6a) The temperature adjustment unit 21a determines whether it is within the data acquisition period for temperature adjustment. If it is within the data acquisition period for temperature adjustment, the process proceeds to step S2a. If it is not within the data acquisition period for temperature adjustment, the process proceeds to step S7a.

(S7a) The temperature adjuster 21a calculates the maximum temperature tmp_max used in the equations (6) and (7) based on the temperature histogram 80 (or cumulative histogram 81) generated as a result of the data collection process in step S3a. do. The temperature adjuster 21a uses the calculated maximum temperature tmp_max to calculate a new temperature tmp[i] based on equations (6) and (7). The temperature adjuster 21a outputs new temperature information indicating the calculated new temperature and a temperature setting signal to the temperature controller 22a and the state controller 23a. The state control unit 23a receives the new temperature information and the temperature setting signal output by the temperature adjustment unit 21a, and updates the temperature associated with each temperature index in the first correspondence information held by the state control unit 23a. .

(S8a) The temperature control unit 22a outputs the new temperature information and the temperature setting signal to each of the search units 10a1 to 10aN to set the temperature, and each of the search units 10a1 to 10aN executes probabilistic search processing. Let

(S9a) When the search units 10a1 to 10aN execute probabilistic search for a specified time or a specified number of iterations, the search units 10a1 to 10aN determine the energy value, bit state, and local field for each adjacent search unit. It is transmitted to the state control section 23a. The state control unit 23a acquires the energy values, bit states, and local fields calculated by the search units 10a1 to 10aN for each adjacent search unit.

(S10a) The state control unit 23a performs state exchange control based on the exchange probability based on the formula (5) using the energy difference between the search units with adjacent temperatures. The state control unit 23a performs state exchange control for each pair of search units having adjacent temperatures.

(S11a) The search units 10a1 to 10aN determine whether or not there is no change in the bit state in the minimum temperature search units for the prescribed number of times. When there is no change in the bit state in the searching section with the lowest temperature, the searching sections 10a1 to 10aN output the bit state to the general control section 24a, and complete the overall control processing of replica exchange. If there is a change in the bit state in the search unit with the lowest temperature, the search units 10a1 to 10aN proceed to step S8a and continue the stochastic search processing.

FIG. 22 is a flowchart illustrating an example of data collection processing.
The data collection process corresponds to step S3a. Although the procedure for the search unit 10a1 by the temperature adjustment unit 21a will be described below, the same procedure is applied to the search units 10a2 to 10aN. Steps S31a to S34a described below are executed for each of the search units 10a1 to 10aN. One temperature histogram 80 in step S34a is calculated for each of the search units 10a1 to 10aN.

(S30a) The minimum energy update confirmation circuit 320 determines whether or not it is time to collect data. If it is the data collection timing, the process proceeds to step S31a. If it is not the data collection timing, the data collection process ends. As described above, the data collection timing may be the timing each time the search processing (procedure in FIG. 12) of the search units 10a1 to 10aN is completed, or the timing each time the search processing is completed a plurality of times.

(S31a) The minimum energy update confirmation circuit 320 acquires the energy E1 and the replica _number from the search unit 10a1. The minimum energy update confirmation circuit 320 compares the minimum energy of the corresponding replica _number stored in the register 310 with the acquired energy E1, and determines whether or not the minimum energy has been updated. When the minimum energy is updated, the minimum energy update confirmation circuit 320 updates the record of the minimum energy of the corresponding replica number stored in the register 310 to the energy E1 obtained this time from the search unit 10a1, and step _S34a . is processed. If the minimum energy has not been updated, the process proceeds to step S32a.

(S32a) The maximum temperature update confirmation circuit 330 acquires the temperature set in the search unit 10a1 and determines whether the maximum temperature for the corresponding replica number stored in the register 310 has been updated. If the maximum temperature has been updated, the process proceeds to step S33a. If the maximum temperature has not been updated, data collection processing for that replica number ends.

(S33a) The maximum temperature update confirmation circuit 330 updates the record of the maximum temperature of the corresponding replica number stored in the register 310 to the temperature set in the search section 10a1. Then, the data collection processing for the corresponding replica number ends.

(S34a) The temperature histogram calculation circuit 340 reads the maximum temperature corresponding to the replica number from the register 310, and adds 1 to the frequency (frequency) of the maximum temperature in the temperature histogram 80. As described above, one temperature histogram 80 is generated for each of the search units 10a1 to 10aN (N bit states). Also, the maximum temperature update confirmation circuit 330 updates the record of the maximum temperature of the corresponding replica number stored in the register 310 to the temperature currently set in the searching unit 10a1. Then, the data collection processing for the corresponding replica number ends.

Note that the temperature adjuster 21a may execute the processes of steps S31a to S34a in parallel for each of the searchers 10a1 to 10aN. Alternatively, the temperature adjuster 21a may sequentially select one of the searchers 10a1 to 10aN and repeat the processes of steps S31a to S34a.

In this manner, the temperature adjustment unit 21a acquires the energy value from each of the search units 10a1 to 10aN after the number of repetitions of the search for the ground state of the energy value has been reached or after a certain period of time has elapsed. Then, the temperature adjustment unit 21a confirms whether or not the minimum value of the energy value has been updated with respect to the bit states (values of a plurality of state variables) in each of the search units 10a1 to 10aN, thereby performing data collection processing. I do.

FIG. 23 is a flowchart showing an example of exchange control.
Exchange control corresponds to steps S5a and S10a.
(S40a) The state control unit 23a exchanges the bit state and the local field with the adjacent upper (or lower) temperature search unit for the even-numbered search unit based on the exchange probability shown in equation (5). determine whether or not The decision to swap bitstates and local fields is made for each pair of searchers. The function f of the equation (5) uses the function of the Metropolis method of the equation (2) or the function of the Gibbs method of the equation (3). If there is a pair of search units determined to exchange bit states and local fields, the process proceeds to step S41a. If no searcher pair is determined to exchange bitstates and local fields, processing proceeds to step S42a.

(S41a) The state control unit 23a exchanges the bit state and local field for the pair of search units determined to exchange the bit state and local field in step S40a. The state control unit 23a updates the aforementioned third correspondence information held by the state control unit 23a according to the state exchange.

(S42a) The state control unit 23a exchanges the bit state and the local field with the adjacent upper (or lower) temperature search unit for the odd-numbered search units based on the exchange probability shown in Equation (5). determine whether or not The decision to swap bitstates and local fields is made for each pair of searchers. The function f of the equation (5) uses the function of the Metropolis method of the equation (2) or the function of the Gibbs method of the equation (3). When the state control unit 23a determines in step S40a whether or not to exchange the state of the even-numbered search unit with the higher temperature search unit, in step S42a, the state control unit 23a determines whether or not to exchange the state of the even-numbered search unit with the higher temperature search unit. Determines whether to exchange the state with When the state control unit 23a determines in step S40a whether or not to exchange the temperature of the even-numbered search unit with the lower temperature search unit, in step S42a, the state control unit 23a changes the state of the odd-numbered search unit with the lower temperature search unit. determines whether or not to replace the If there is a pair of search units determined to exchange bitstates and local fields, processing proceeds to step S43a. If no searcher pair is determined to exchange bitstates and local fields, exchange control ends.

(S43a) The state control unit 23a exchanges the bit state and local field for the pair of search units determined to exchange the bit state and local field in step S42a. The state control unit 23a updates the third correspondence information held by the state control unit 23a according to the state exchange. Then, the exchange control ends.

In the above example, the state exchange control is performed by focusing on the even-numbered search unit and then the odd-numbered search unit. Focusing on this, state exchange control may be performed. That is, steps S40a and S41a may be executed after steps S42a and S43a.

In this way, the optimization device 2 may perform the ground state search of the Ising model by exchanging the states between the search units in the replica exchange.
According to the optimization device 2, the temperatures to be set in the searching units 10a1 to 10aN can be appropriately determined. Specifically, the maximum value of the new temperature tmp[i] is determined based on the update of the minimum energy in the data acquisition period and the statistical information of the set maximum temperature, and the temperature set for each search unit can be prevented from being too high or too low. Therefore, the solution accuracy in the optimization device 2 can be improved. In addition, by improving the solution accuracy, it is possible to increase the possibility of reaching an appropriate solution more quickly and speed up the calculation.

In addition, in order to determine an appropriate maximum temperature (temperature corresponding to tmp_max), it is conceivable that the optimization process by the optimization device 2 is repeatedly executed and the user manually adjusts. It takes a lot of work. On the other hand, by determining the maximum temperature tmp_max based on the temperature statistical information as described above, it is possible to reduce the trouble of temperature adjustment by the user.

Furthermore, similarly to the first embodiment, the temperature adjustment function in the optimization device 2 may be realized by software processing by the CPU. The optimization device 2 can also have the same hardware configuration as the optimization device 1a. However, the probabilistic search unit performs control to exchange states between search units in the replica exchange.

FIG. 24 is a diagram showing an example of the number of solutions.
A graph 90 shows the number of solutions to the combinatorial optimization problem obtained when the temperature is determined and the calculation is performed by the method of the comparative example, and the temperature adjustment by the optimization devices 1 and 2 (or the optimization device 1a). and the number of solutions to the combinatorial optimization problem obtained when performing calculations. The horizontal axis of graph 90 indicates the problem and the vertical axis indicates the number of solutions. The method of the comparative example is a method of determining the maximum temperature by a predetermined calculation based on the coefficient matrix W representing the coupling between spin bits at the start of calculation, and determining the temperature to be set in each search unit.

The experimental conditions are as follows. The total number of iterations of the ground state search is 10 million. The number of replicas (corresponding to the number of search units 10a1 to 10aN) is 100. The increment value of the offset value used for escaping from the local solution is 1000 by the offset controller of each search unit. In the experiment, a combinatorial optimization problem whose solution is known in advance is used, and after the total number of iterations of the ground state search is completed, the number of search units for which the solution is obtained is counted.

Here, the character string attached to the horizontal axis is the name of the question, and the prefix indicated by an alphabet or a combination of an alphabet and a number indicates the type of question. For example, the prefix "mcp" indicates a max-cut problem. The prefix "molsim" indicates a molecular similarity problem. The prefix "tsp32" denotes the Traveling Salesman Problem. Additionally, the string following the prefix indicates variations in that type of problem.

Graph 90 shows an increase in solutions in the molecular similarity problem (“molsim_950_XX”) and the traveling salesman problem (“tsp32_mapXX”). In addition, regarding the maximum cut problem, it can be seen that several variations (eg, mcp_G51 to mcp_G54) have almost the same solution-finding performance as the method of the comparative example. Regarding the graph 90, it can be seen that the methods of the optimization devices 1 and 2 tend to improve compared to the method of the comparative example, and the solution-finding performance is improved. Moreover, since the number of solutions increases, the possibility of reaching the optimum solution earlier than in the method of the comparative example increases, and the speed of calculation can be increased.

1 optimization device 10a1, 10a2, .

Claims (10)

In an optimization device having a plurality of search units and a control unit that controls the plurality of search units,
Each of the plurality of search units,
a state holding unit holding values of a plurality of state variables included in an evaluation function representing an energy value;
Energy calculation for performing a ground state search by calculating a change value of the energy value for each of the plurality of state transitions when the state transition occurs in response to a change in any of the plurality of state variable values. Department and
Based on the set temperature value, the change value, and a random value, it is determined stochastically whether to accept one of the plurality of state transitions according to the relative relationship between the change value of the energy value and the thermal excitation energy. and a transition control unit for
The control unit
A temperature for acquiring temperature statistical information, which is statistical information relating to temperature value transitions in each of the plurality of search units, and determining the temperature values to be set in each of the plurality of search units based on the acquired temperature statistical information. an adjustment unit;
a temperature control unit that sets the determined temperature value to each of the plurality of search units;
an exchange control unit that exchanges the temperature values or the values of the plurality of state variables among the plurality of search units after reaching the number of repetitions of the ground state search for the energy value or after a predetermined time has elapsed;
an optimization device having The temperature adjustment unit searches the plurality of temperature values corresponding to the maximum value of the appearance frequency in the temperature frequency information obtained by counting the appearance frequency of each temperature value regarding the transition of the temperature values among the acquired temperature statistical information. set for each of the divisions,
2. The optimization device of claim 1. The temperature adjusting unit multiplies the maximum value of the cumulative frequency by a predetermined coefficient in the temperature cumulative frequency information representing the cumulative frequency of occurrence of each temperature value regarding the transition of the temperature value among the acquired temperature statistical information. setting a temperature value corresponding to the frequency obtained in each of the plurality of search units;
2. The optimization device of claim 1. The predetermined coefficient is input from the outside,
4. The optimization device according to claim 3. The transition control unit probabilistically determines whether to accept one of the plurality of state transitions according to the relative relationship between the change value and the thermal excitation energy based on the temperature value, the change value, and a random value. When determining, adding a predetermined offset value to the change value of the energy value;
5. An optimization device according to any one of claims 1-4. The temperature adjustment unit determines a maximum value of the temperature values to be set in each of the plurality of search units from the acquired temperature statistical information, and sets the temperature value in each of the plurality of search units based on the maximum value. determining temperature values other than the highest value,
6. An optimization device according to any one of claims 1-5. When the minimum value of the energy value is updated in any one of the search units, the temperature adjustment unit performs obtaining the highest temperature value set for the values of the plurality of state variables as temperature statistics;
7. Optimization apparatus according to any one of claims 1-6. The temperature adjustment unit acquires the energy value from each of the plurality of search units after reaching the number of repetitions of the ground state search for the energy value or after a predetermined time has elapsed, and determines whether the minimum value of the energy value has been updated. against each of the plurality of search units or the values of the plurality of state variables in each of the plurality of search units;
8. Optimization device according to claim 7. The temperature adjustment unit acquires temperature statistical information during a predetermined period in which a first temperature value is set for each of the plurality of search units, and after the predetermined period ends, based on the temperature statistical information, the plurality of determining a second temperature value to be set for each of the search units;
9. An optimization device according to any one of claims 1-8. In a control method for an optimization device having a plurality of search units and a control unit that controls the plurality of search units,
A state holding unit included in each of the plurality of search units holds values of a plurality of state variables included in an evaluation function representing an energy value,
When a state transition occurs in response to a change in the value of one of the plurality of state variables, the energy calculation unit included in each of the plurality of search units calculates the change value of the energy value for each of the plurality of state transitions. perform a ground state search by computing for
A transition control unit included in each of the plurality of search units determines the plurality of states according to the relative relationship between the change value of the energy value and the thermal excitation energy based on the set temperature value, the change value, and the random value. determining probabilistically whether to accept any of the transitions;
A temperature adjusting unit included in the control unit acquires temperature statistical information that is statistical information about transition of temperature values in each of the plurality of searching units, and based on the acquired temperature statistical information, each of the plurality of searching units determine the temperature value to set to
A temperature control unit included in the control unit sets the determined temperature value to each of the plurality of search units;
An exchange control unit included in the control unit exchanges the temperature value or the values of the plurality of state variables between the plurality of search units after the number of repetitions of the ground state search for the energy value has been reached or after a certain period of time has elapsed.
How to control the optimizer.

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